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Computing the Conditional Probability of an Event

  • 1.

    An algebra class has both juniors and seniors in it, 51% are juniors. On a recent test, 64% of all students scored an A. In the class, 22% are juniors who scored an A. Looking at a random student, what is the probability they scored an A, given that they are a junior? Select the closest answer.

    Answers:

    • 34.5%

    • 22.9%

    • 11.3%

    • 43.1%

  • 2.

    An algebra class has both juniors and seniors in it, 64% are juniors. On a recent test, 64% of all students scored an A. In the class, 22% are juniors who scored an A. Looking at a random student, what is the probability they are a junior, given that they scored an A? Pick the best answer.

    Answers:

    • 95.3%

    • 43.5%

    • 34.4%

    • 22.0%

  • 3.

    Students are gathering weather information for July and September. They found that of the temperature measurements taken, 20% are in July and are below 80. In the data, 60% of the measurements are from July. What is the probability that a temperature was below 80, if we know the month was July? Choose the closest answer.

    Answers:

    • 40%

    • 25%

    • 3%

    • 33.3%

  • 4.

    Students are gathering weather information for days in June and August. They found that of the temperature measurements taken, 30% are in June and are below 80 degrees. In the data, 60% of the measurements are from June. A random day is chosen in June, what is the probability that it had a temperature below 80? Pick the best answer.

    Answers:

    • 50%

    • 80%

    • 60%

    • 30%

  • 5.

    In a survey, men and women were asked if they prefer dogs or cats as pets. In the survey, 45% of the answers were from men. Also, 5% of the survey results were men that prefer cats. If a random person chosen is a man, what is the probability that they prefer cats? Select the closest answer.

    Answers:

    • 11%

    • 45%

    • 40%

    • 5%

  • 6.

    In a survey, men and women were asked if they prefer dogs or cats as pets. In the survey, 40% of the answers were women who showed a preference for cats. Also, the survey showed that 45% of people prefer cats. A random person is chosen that prefers cats. What is the probability they are a woman? Pick the best answer.

    Answers:

    • 89%

    • 67%

    • 5%

    • 40%

  • 7.

    In a car dealership, 17% of cars are new. At the dealership, 30% of cars are red. Of all the cars, 6% are new and red. If a random car is red, what is the probability it is new? Choose the closest answer.

    Answers:

    • 36%

    • 17%

    • 43%

    • 20%

  • 8.

    In a car dealership, 17% of cars are new. Of all cars, 40% are red. Also, 6% cars are new and red. Given that a randomly chosen car is new, what is the probability it is red? Select the closest answer.

    Answers:

    • 15%

    • 6.8%

    • 42.5%

    • 35.3%

  • 9.

    In a season, a football team plays 20% of their games at night. During the season, the team won 70% of their games. Also, 7% of games were played at night and won. What is the probability that the team won, if you know they played at night? Pick the best answer.

    Answers:

    • 10%

    • 35%

    • 70%

    • 14%

  • 10.

    In a season, a football team plays 20% of their games during the day. During the season, the team lost 70% of their games. Also, 9% of games were played during the day and lost. What is the probability that the team lost, given it was a day game? Select the best answer.

    Answers:

    • 29%

    • 45%

    • 35%

    • 18%

  • 11.

    After a wedding, there was a case of food poisoning. Half (50%) of the guests got sick. The food options were fish or chicken, 46% of the people ate fish. Also, 38% of the people ate fish and got sick. Given that a person got sick, what is the probability they ate fish? Choose the closest answer.

    Answers:

    • 19%

    • 76%

    • 23%

    • 38%

  • 12.

    After a wedding, there was a case of food poisoning. Half (50%) of the guests got sick. The food options were fish or chicken, 26% of all people ate fish. Also, 18% of the people ate fish and got sick. Given that a person ate fish, what is the probability they got sick? Select the closest answer.

    Answers:

    • 30.8%

    • 69.2%

    • 9.0%

    • 13.1%

  • 13.

    A manager started keeping track of the times workers showed up. One day, 26% of the workers showed up late. Overall, 70% of workers drive to work. On this day, 10% of workers both drove and were late. Knowing that a random worker drove to work, what is the probability they were late? Pick the best answer.

    Answers:

    • 14.3%

    • 61.5%

    • 38.5%

    • 7.0%

  • 14.

    A manager started tracking if workers were on time. One day, 74% of the workers showed up early. Overall, 60% of workers drove to work. On this day, 20% of workers drove and were early. Knowing that a random worker was early, what is the probability they drove? Select the closest answer.

    Answers:

    • 14.8%

    • 27.0%

    • 33.3%

    • 72.9%

  • 15.

    A survey found that 71.4% of Americans desire stronger gun laws. In this survey, 50.9% of the answers were from Missouri. 23.7% of survey responses were from people from Missouri who desire stronger gun laws. Suppose a random person who desires stronger gun laws is chosen. What is the probability this person is from Missouri? Pick the best answer.

    Answers:

    • 46.6%

    • 66.8%

    • 33.2%

    • 71.3%

  • 16.

    A survey found that 71.4% of Americans desire stronger gun laws. In this survey, 50.9% of the answers were from Missouri. 40.7% of people are from Missouri and desire stronger gun laws. Suppose a random person from Missouri is chosen. What is the probability this person desires stronger gun laws? Choose the closest answer.

    Answers:

    • 41%

    • 80%

    • 57%

    • 71%

  • 17.

    In Paris, the probability that a married man drives is 90%. If the probability that the married man and his spouse both drive is 85%, what is the probability the spouse drives, given that the man drives? Select the best answer.

    Answers:

    • 85.0%

    • 5.0%

    • 94.4%

    • 76.5%

  • 18.

    The probability that Joe studies and passes their test is 80%. If the probability that Joe studies at all is 83%. Assuming that Joe studied, what is the probability they passed the test? Choose the closest answer.

    Answers:

    • 3%

    • 96.4%

    • 66.4%

    • 7%

  • 19.

    The probability that Joe studies and passes his test is 63% and there is a 17% chance he studies and fails the test. The probability that Joe studies at all is 80%. Assuming that Joe studied, what is the probability he failed? Choose the closest answer.

    Answers:

    • 21.3%

    • 63.1%

    • 96.4%

    • 20.5%

  • 20.

    Testing for weight and blood pressure in a retirement community, the probability that a man is overweight is 42%. In addition, the probability that a man has high blood pressure and is overweight is 28%. By choosing a random man who is overweight, what is the probability he has high blood pressure? Select the best answer.

    Answers:

    • 33.3%

    • 66.7%

    • 11.8%

    • 14.0%

  • 21.

    In one health club, 75% of members use treadmills. In this club, 50% of members are there to lift weights. Overall, 30% of members use treadmills and are also there to lift weights. If a random member is chosen, what is the probability they use a treadmill given that they are there to lift weights? Pick the closest answer.

    Answers:

    • 25%

    • 37.5%

    • 60%

    • 22.5%

  • 22.

    In one health club, 75% of members use treadmills. In this club, 40% of members are there to lift weights. Overall, 30% of members use treadmills and are also there to lift weights. If a random member is chosen, what is the probability they are there to lift weights given that they use a treadmill? Choose the best answer.

    Answers:

    • 75%

    • 27%

    • 53%

    • 40%

  • 23.

    In a recent survey of voters, 53% of participants were women while 47% were men. Just focusing on two political parties, 37% voted Republican. 20% of voters were men and voted Republican. Given that a voter was Republican, what is the probability it was a man? Select the best answer.

    Answers:

    • 54%

    • 63%

    • 38%

    • 89%

  • 24.

    In a recent survey of voters, 53% of participants were women while 47% were men. Just focusing on two political parties, 39% voted Democrat. There was a 22% chance that a voter was a woman who voted Democrat. Given that a voter was a woman, what is the probability she was a Democrat? Pick the closest answer.

    Answers:

    • 21%

    • 89%

    • 42%

    • 74%

  • 25.

    In a special deck of cards, 10% are Kings. There are four different suits, so 25% of the cards are hearts. The probability that the card is a King and a heart is 7%. Given that a card is a heart, what is the probability it is a King? Select the best answer.

    Answers:

    • 40%

    • 28%

    • 3.5%

    • 7.7%

  • 26.

    In a special deck of cards, 10% are Aces. There are four different suits, so 25% of the cards are hearts. The probability that the card is an Ace and a heart is 7%. Given that a card is an Ace, what is the probability it is a heart? Choose the closest answer.

    Answers:

    • 70%

    • 40%

    • 15%

    • 28%

  • 27.

    In a survey, men and women were asked if they prefer dogs or cats as pets. In the survey, 45% of the answers were from men. The survey also found that overall 20% prefer cats. The survey showed that 5% of people are men who prefer cats. If a random person chosen prefers cats, what is the probability it is a man? Select the closest answer.

    Answers:

    • 44%

    • 25%

    • 11%

    • 15%

  • 28.

    An algebra class has both juniors and seniors in it, 71% are juniors. On a recent test, 64% of all students scored an A. In the class, 39% are juniors who scored an A. Looking at a random student, what is the probability they scored an A, given that they are a junior? Select the closest answer.

    Answers:

    • 61%

    • 55%

    • 90%

    • 45%

  • 29.

    After a party, there was a case of food poisoning. 80% of the guests got sick. The food options were fish or chicken, 36% of all people ate chicken. Also, 18% of the people ate chicken and got sick. Given that a person got sick, what is the probability they ate chicken? Select the closest answer.

    Answers:

    • 28.8%

    • 45.0%

    • 22.5%

    • 50.0%

  • 30.

    At the swimming pool, 30% of people there are children and 70% are adults. Of the people, 17.8% were children wearing sunscreen. Of the adults 25% are wearing sunscreen. What is the probability a randomly selected child is wearing sunscreen? Pick the best answer.

    Answers:

    • 41.6%

    • 17.8%

    • 59.3%

    • 35.7%

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