Using Probabilities to Identify Independent Events

  • 1.

    Some roommates divided up chores by writing the chores on slips of paper and putting them in a hat. The first roommate pulls "Washing dishes" out of the hat, which they had a 25% chance to do so. The second roommate pulls out "Take out the trash", which had the probability of 33%. What of the following is true?

    Answers:

    • These are independent events because the probability of choosing "take out the trash" was not affected by the first pull.

    • These are independent events because the probability of choosing "take out the trash" was affected by the first pull.

    • These are dependent events because the probability of choosing "take out the trash" was not affected by the first pull.

    • These are dependent events because the probability of choosing "take out the trash" was affected by the first pull.

  • 2.

    Maris is rolling a six-sided dice. Her first roll is a 3. Her second roll is a 5. Are these independent or dependent events?

    Answers:

    • Dependent. Her first roll did affect the probability of her second roll.

    • Independent. Her first roll did not affect the probability of her second roll.

    • Dependent. Her first roll did not affect the probability of her second roll.

    • Independent. Her first roll did affect the probability of her second roll.

  • 3.

    Katlyn is randomly pulling unique colored pencils out of a pencil bag and not replacing them. She first pulls out a red color pencil, which she had a 1 in 20 chance of doing so. What is the probability of selecting the next colored pencil on her second pull, as well as the type of probability event?

    Answers:

    • 1 in 19. This is a dependent event.

    • 1 in 20. This is a dependent event.

    • 1 in 19. This is an independent event.

    • 1 in 20. This is an independent event.

  • 4.

    Liam has a deck of 52 playing cards. He shuffles, and pulls the top card. Then he puts the card back in the deck, shuffles, and pulls the top card again. What is true about the probability of the second card?

    Answers:

    • The probability of the second card is affected by what he pulled before. These are independent events.

    • The probability of the second card is affected by what he pulled before. These are dependent events.

    • The probability of the second card is not affected by what he pulled before. These are dependent events.

    • The probability of the second card is not affected by what he pulled before. These are independent events.

  • 5.

    Mira is doing a survey of how many people in each cycling class at the gym wear red shorts. 40% of the first class are wearing red shorts, while only 20% of the second class are wearing red shorts. Which of the following is true?

    Answers:

    • These are independent events as the probability of red shorts in the second class are not affected by the first class.

    • These are dependent events as the probability of red shorts in the second class are not affected by the first class.

    • These are independent events as the probability of red shorts in the second class is affected by the first class.

    • These are dependent events as the probability of red shorts in the second class is affected by the first class.

  • 6.

    Nadia likes to randomly select the shirt she'll wear for each day out of her closet. On Monday, she had a 5% chance of picking a white shirt. On Tuesday, she had a 10% chance of picking a white shirt. And on the third day, there was a 15%. What can be derived from this?

    Answers:

    • These are independent events, as what she picks in the earlier days affect the probability of later days.

    • These are independent events, as what she picks in the earlier days does not affect the probability of later days.

    • These are dependent events, as what she picks in the earlier days affect the probability of later days.

    • These are dependent events, as what she picks in the earlier days does not affect the probability of later days.

  • 7.

    Mike is playing a dice rolling game. He rolls badly the first 10 times, therefore he believes the probability of rolling better on the eleventh roll is higher. Is Mike correct, and why or why not?

    Answers:

    • Mike is not correct. These are independent events and therefore the probability will not change.

    • Mike is not correct. These are dependent events and therefore the probability will not change.

    • Mike is correct. These are dependent events and therefore the probability will change.

    • Mike is correct. These are independent events and therefore the probability will change.

  • 8.

    A video game has a random prize generator each time you win a match. There are 20 possible items to win, and this particular game does not give duplicate prizes. If there is a 5% chance to win any item the first time you use the prize generator, what can be said about the probability of the following prizes and why?

    Answers:

    • The probability of receiving the following prizes will not change as these are dependent events.

    • The probability of receiving the following prizes will not change as these are independent events.

    • The probability of receiving the following prizes will change as these are dependent events.

    • The probability of receiving the following prizes will change as these are independent events.

  • 9.

    Tori uses a random number generator. The first time, it gives her the number 7. The second time, it also gives her the number 7. What can be said about these events?

    Answers:

    • These are dependent events. Getting 7 the first time did affect the probability of her getting 7 the second time.

    • These are dependent events. Getting 7 the first time did not affect the probability of her getting 7 the second time.

    • These are independent events. Getting 7 the first time did not affect the probability of her getting 7 the second time.

    • These are independent events. Getting 7 the first time did affect the probability of her getting 7 the second time.

  • 10.

    There is a snack drawer at an office that is replenished every Monday. If employees randomly select snacks at a consistent rate, and there is a 10% chance of getting a bag of trail mix on Tuesday, what can be said about the probability of getting trail mix on Thursday?

    Answers:

    • The probability of getting trails mix on Thursday will be different than on Tuesday, as these are independent events.

    • The probability of getting trails mix on Thursday will be the same than on Tuesday, as these are independent events.

    • The probability of getting trails mix on Thursday will be different than on Tuesday, as these are dependent events.

    • The probability of getting trails mix on Thursday will be the same than on Tuesday, as these are dependent events.

  • 11.

    Gina rolls a 6 on her first dice roll on a six-sided dice. What is the probability that she'll roll a 5 on her second roll, and why?

    Answers:

    • 1 in 6, because these are independent events.

    • 1 in 5, because these are dependent events.

    • 1 in 6, because these are dependent events.

    • 1 in 6, because these are independent events.

  • 12.

    Dan does a coin flip and gets heads. He then rolls a dice, and gets a 4. What can be said about these events?

    Answers:

    • They are independent events, as the coin flip did affect the probability of the dice roll.

    • They are dependent events, as the coin flip did not affect the probability of the dice roll.

    • They are independent events, as the coin flip did not affect the probability of the dice roll.

    • They are dependent events, as the coin flip did affect the probability of the dice roll.

  • 13.

    Ella saw on the weather report there'd be a 60% chance of rain the next day. When it did rain the next day, she then noticed that 75% of her classmates brought umbrellas. What can be said about these events?

    Answers:

    • These are dependent events, as the outcome of the first event affected the second event.

    • These are independent events, as the outcome of the first event didn't affect the second event.

    • These are dependent events, as the outcome of the first event didn't affect the second event.

    • These are independent events, as the outcome of the first event affected the second event.

  • 14.

    Matthew does not know the answer for a question on an online multiple choice test. The order of the answer choices with each question is completely randomized by a computer. Matthew reasons that since the last question's answer was A, the probability that the answer will be A again is less. What can be said about Matthew's reasoning?

    Answers:

    • Matthew is wrong. The probability will remain the same as these are independent events.

    • Matthew is correct. The probability will change as these are dependent events.

    • Matthew is wrong. The probability will remain the same as these are dependent events.

    • Matthew is correct. The probability will change as these are independent events.

  • 15.

    Taja draws a name out a hat and does not replace them. If there was a 6% chance to pull any name on the first draw, what is true about the probability of the following draws and why?

    Answers:

    • The probability to pull any name will remain the same, as these are independent events.

    • The probability to pull any name will increase, as these are dependent events.

    • The probability to pull any name will increase, as these are independent events.

    • The probability to pull any name will remain the same, as these are dependent events.

  • 16.

    Undine goes to a store and sees they have 50% of their soda stock. She then goes to another store, and sees they have 70% of their candy stock. What of the following statements is true?

    Answers:

    • These are independent events, as the probability of these events do influence each other.

    • These are dependent events, as the probability of these events do not influence each other.

    • These are dependent events, as the probability of these events do influence each other.

    • These are independent events, as the probability of these events do not influence each other.

  • 17.

    A group of children are drawing straws to decide who'll clean the toy bin. If Nori first draws a long straw, what can be said about the probability of Dana drawing the short straw?

    Answers:

    • The probability of Dana drawing the short straw has increased, as these are dependent events.

    • The probability of Dana drawing the short straw remains the same, as these are dependent events.

    • The probability of Dana drawing the short straw remains the same, as these are independent events.

    • The probability of Dana drawing the short straw has increased, as these are independent events.

  • 18.

    Haley notices that only 30% of the kids in her reading club have ponytails, while 60% of her chess club have ponytails. What is true about this statement?

    Answers:

    • These are independent events, because the probability of the reading club results does affect the chess club.

    • These are dependent events, because the probability of the reading club results does not affect the chess club.

    • These are independent events, because the probability of the reading club results does not affect the chess club.

    • These are dependent events, because the probability of the reading club results does not affect the chess club.

  • 19.

    There are 10 apples, 4 green and 6 red. Margit randomly selects a red apple. After eating that one, if Margit decides to randomly select another apple from the same group of apples and gets a green apple, what type of events are these and why?

    Answers:

    • Dependent events. The probability of what she selected the second time was influenced by the first apple she picked.

    • Independent events. The probability of what she selected the second time was not influenced by the first apple she picked.

    • Independent events. The probability of what she selected the second time was influenced by the first apple she picked.

    • Dependent events. The probability of what she selected the second time was not influenced by the first apple she picked.

  • 20.

    Teresa spins a spinner that randomly selects between 4 different colors each time. What type of events is each spin, and why?

    Answers:

    • Independent events. The probability of selecting one color does not change with each spin.

    • Dependent events. The probability of selecting one color does not change with each spin.

    • Independent Events. The probability of selecting one color does change based on what she spun before.

    • Dependent Events. The probability of selecting one color does change based on what she spun before.

  • 21.

    Ms. Sisko has popsicle sticks with the students names in a cup. When she wants to call on a student, she'll pull a stick out at random, and then wait until the end of class to put the stick back so she only calls on a student once per class. If Mario is not called on the first time, what can be said about the probability that he'll be called on later on in the class with each pull, and why?

    Answers:

    • The probability that he'll be called on won't increase each time, as these are dependent events.

    • The probability that he'll be called on will increase each time, as these are dependent events.

    • The probability that he'll be called on won't increase each time, as these are independent events.

    • The probability that he'll be called on will increase each time, as these are independent events.

  • 22.

    A video game has a random prize generator, with there being a 1% chance each time that you'll win a S-rank item. If you do not pull the S-rank item the first time, and the prize pool resets each time - what is the probability that you'll draw an S-rank item the second time and why?

    Answers:

    • 2%, because these are dependent events that affect each other.

    • 2%, because these are independent events that affect each other.

    • 1%, because each time is an independent event that don't affect each other.

    • 1%, because these are dependent events that don't affect each other.

  • 23.

    Peter pulled a blue marble out of a bag. He set it aside, and then pulled out a green marble. What can be said about these events?

    Answers:

    • They are independent events because Peter pulling the blue marble didn't affect the probability of pulling the green marble.

    • They are dependent events because Peter pulling the blue marble affected the probability of pulling the green marble.

    • They are dependent events because Peter pulling the blue marble didn't affect the probability of pulling the green marble.

    • They are independent events because Peter pulling the blue marble affected the probability of pulling the green marble.

  • 24.

    While working at a call center that calls phone numbers that are randomly generated, Dominika noticed one night that only 12% of the people she randomly called answered. The following night, 20% of the people she called answered. What can be said about these events?

    Answers:

    • They are dependent events, as the probability of people answer on the second night was not affected by the first.

    • They are independent events, as the probability of people answer on the second night was not affected by the first.

    • They are independent events, as the probability of people answer on the second night was affected by the first night.

    • They are dependent events, as the probability of people answer on the second night was affected by the first night.

  • 25.

    Sara pulled a caramel out of a bag of assorted candies, which she had a 10% chance of doing so. After she ate that candy, she pulled out another candy. What can be said about the probability of her pulling out another caramel, and why?

    Answers:

    • The probability of pulling another caramel will be the same, as these are independent events.

    • The probability of pulling another caramel will decrease, as these are dependent events.

    • The probability of pulling another caramel will be the same, as these are dependent events.

    • The probability of pulling another caramel will decrease, as these are independent events.

  • 26.

    Crow is spinning a spinner with different colors, with each color having a 12% chance of being selected on the first spin. Crow believes that since blue wasn't picked on the first spin, the probability of it landing on blue the second time will still be 12%. Is Crow right and why?

    Answers:

    • Crow is correct. These are independent events and the probability isn't affected by the first spin.

    • Crow is correct. These are dependent events and the probability isn't affected by the first spin.

    • Crow is wrong. These are independent events and the probability is affected by each spin.

    • Crow is wrong. These are dependent events and the probability is affected by each spin.

  • 27.

    During a bingo game, a random combination of a letter and number is called out. If that combination is not repeated, what statement is true about the probability of different combinations being called each time?

    Answers:

    • The probability of different combinations being called will not increase because they're independent events.

    • The probability of different combinations being called will increase as these are independent events.

    • The probability of different combinations being called will increase as these are dependent events.

    • The probability of different combinations being called will not increase because they're dependent events.

  • 28.

    Jack has a 1:52 chance of pulling an ace of spades from a card deck, but instead draws a queen of hearts. If he replaces each card he draws back into the deck and shuffles, what chance does he have to pull an ace of spade on the second draw?

    Answers:

    • 1:52 because these are independent events that don't influence each other.

    • 1:51 because these are dependent events that influence each other.

    • 1:51 because these are independent events that influence each other.

    • 1:52 because these are dependent events that don't influence each other.

  • 29.

    50% of the students in the class brought their own lunch. During lunch time, 30% of the entire class ate sandwiches made at their homes. Are these independent or independent events, and why?

    Answers:

    • Dependent event, as the students eating sandwiches from home had nothing to do with the students who brought lunches.

    • Dependent events, as the outcome of how many students brought their own lunch affected how many ate sandwiches made at home.

    • Independent event, as the students eating sandwiches from home had nothing to do with the students who brought lunches.

    • Independent events, as the outcome of how many students brought their own lunch affected how many ate sandwiches made at home.

  • 30.

    Diana rolls 4 six-sided dice, and gets a sum totaling 20. She then rolls the same 4 dice again, and her next total ends up being 16. What is true about these events?

    Answers:

    • They're dependent events as the first dice roll did not affect the probability of the second.

    • They're independent events as the first dice roll did not affect the probability of the second.

    • The first dice roll did affect the second roll, so they are independent events.

    • The first dice roll did affect the second roll, so they are dependent events.

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