Solving a Word Problem Involving the Probability of an Intersection

  • 1.

    Starting a new school year, 47% of freshman are taking Algebra, while 20% are taking German. We also know that overall, 60% are taking Algebra or German, or both. What is the probability that a student is taking both Algebra AND German?

    Answers:

    • 9.4%

    • 7%

    • 67%

    • 27%

  • 2.

    In a family, 30% attended college. Also 38% of the family works at a bank. We know that 50% of them attended college or work at a bank, or both. What is the probability that someone from the family went to college AND works at a bank?

    Answers:

    • 15%

    • 80%

    • 20%

    • 18%

  • 3.

    In an apartment complex, 50% of people have used the gym. We also know that 29% have used the swimming pool. It turns out that 63% have used one or the other or both. Knowing that, what is the probability that a person used both the gym AND the pool?

    Answers:

    • 79%

    • 14.5%

    • 16%

    • 39.5%

  • 4.

    One day at a vet's office, 75% of the pets got shots. Meanwhile, 50% of the pets had x-rays. Overall, 80% got shots or x-rays, or both. What's the probability that a pet got shots AND x-rays?

    Answers:

    • 125%

    • 45%

    • 15%

    • 37.5%

  • 5.

    This summer, 81% of days were either rainy or windy (or both). More specifically, 65% of the days were rainy while 24% of the days were windy. So what percent of days were both rainy AND windy?

    Answers:

    • 8%

    • 41%

    • 16%

    • 89%

  • 6.

    Each day, there is a 67% chance I will watch something on Hulu. But there is a 50% chance I will watch something on Netflix. Overall, there is a 78% chance I will use one or the other (or both). What is the probability I use Hulu AND Netflix in a day?

    Answers:

    • 33%

    • 117%

    • 39%

    • 28%

  • 7.

    At a car dealership, 83% of cars are SUV's. I also noticed that 15% of cars are red. All together, 90% are SUV's or red, or both. That means the probability a car is an SUV and also red is _____.

    Answers:

    • 12%

    • 8%

    • 68%

    • 98%

  • 8.

    It turns out that 80% of people exercise by running or riding a bike, or both. Specifically, 65% run while 30% ride a bike. Then what percentage of people both run AND ride a bike?

    Answers:

    • 95%

    • 35%

    • 20%

    • 15%

  • 9.

    In my closet, I have a lot of shirts. Overall, 60% are short sleeved, also 60% are white. All together, 79% are short sleeved or white (or both). What is the probability of a shirt being both short sleeved AND white?

    Answers:

    • 60%

    • 120%

    • 41%

    • 19%

  • 10.

    On my bookshelf, 56% of the books are horror or short stories, or both. More specifically, 49% are horror, while 20% are short stories. What is the probability a book is both horror AND short stories?

    Answers:

    • 10%

    • 29%

    • 13%

    • 69%

  • 11.

    In my algebra class, we know that 18% own a cat while 10% own a dog. Furthermore, 23% own one or the other (or both). What is the probability that a cat owns a cat AND a dog ?

    Answers:

    • 23%

    • 5%

    • 28%

    • 13%

  • 12.

    At a recent party, 75% of the people ate a hamburger while 40% ate a hot dog. Then I saw that 97% ate both hamburger or hot dog (or both!). So all together, what percent of people at a hamburger, AND a hot dog?

    Answers:

    • 115%

    • 30%

    • 35%

    • 18%

  • 13.

    Looking at my set of nail polishes, 20% are blue and 30% have glitter in them. In addition, 43% are blue OR have glitter in them (or both). What percent of my set of nail polish is blue AND glitter?

    Answers:

    • 50%

    • 7%

    • 6%

    • 10%

  • 14.

    A recent survey found the following information: 80% of children enjoy reading, 50% enjoy coloring. Most importantly, 92% enjoy one or the other (or both). What percent enjoy reading AND coloring?

    Answers:

    • 30%

    • 38%

    • 40%

    • 68%

  • 15.

    On the first day of school, 40% of students got lost while 50% helped someone else. Also, 65% got lost or helped someone else (or both). What is the probability a student got lost AND helped someone?

    Answers:

    • 20%

    • 90%

    • 10%

    • 25%

  • 16.

    At the grocery store, 60% of people spend bought pasta. Also, 27% bought ice cream. Today it turns out that 75% bought both pasta or ice cream (or both). What is the probability that a person in the store bought pasta AND ice cream?

    Answers:

    • 15%

    • 12%

    • 43%

    • 87%

  • 17.

    On my husband's list of things to watch this week, 46% are police shows while 59% are documentaries. There is a 70% probability he picks something about police OR a documentary (or both)? There is an overlap though, so how many are documentaries about the police. (meaning documentary AND police)

    Answers:

    • 14%

    • 35%

    • 105%

    • 13%

  • 18.

    In a rock band, some members play multiple instruments. Overall, 68% can play the guitar while 30% can play drums. Additionally, the probability that a person can play guitar or drums (or both) is 81. What is the probability a person can play guitar AND drums?

    Answers:

    • 17%

    • 38%

    • 98%

    • 20%

  • 19.

    I'm researching houses, and only 30% are all brick, while 49% have a garage. Overall, 71% of houses are brick or have a garage (or both) ? What's the probability that a house is brick AND has a garage?

    Answers:

    • 15%

    • 19%

    • 79%

    • 8%

  • 20.

    In a group of high school students, 64% know how to to drive. Overall, 70% of students take the bus to school. We also found out that 84% know how to drive or still take the bus (or both). Knowing that, what percent of students know how to drive AND take the bus?

    Answers:

    • 14%

    • 32%

    • 134%

    • 50%

  • 21.

    This summer, 70% of my co-workers went on some sort of vacation. 40% went to a beach, while 55% went to the mountains. What percent of my co-workers went to both the beach AND the mountains?

    Answers:

    • 95%

    • 25%

    • 15%

    • 22%

  • 22.

    Two of the best options for staying cool in the summer are air conditioning (AC) and fans. The electric company discovered that 75% of people used their AC, while 23% used fans. Overall, 94% used one or both of those options. What percent used both AC and fans?

    Answers:

    • 4%

    • 52%

    • 6%

    • 98%

  • 23.

    All of the people invited to a picnic bring something to share. 60% brought chips, and 30% brought cookies. Altogether, 70% percent brought chips OR cookies OR both. What's the probability a person brought chips AND cookies?

    Answers:

    • 30%

    • 90%

    • 18%

    • 20%

  • 24.

    In the US, it's estimated that 66% of the population has brown hair. Also, 43% of people have blue eyes. The percent of the population that has either brown hair, blue eyes, or both is 81%. What percent of people have brown hair AND blue eyes?

    Answers:

    • 23%

    • 109%

    • 28%

    • 38%

  • 25.

    I'm looking for a cookie that has chocolate chips, AND oats. In my recipe book, 65% of cookies have chocolate chips while 36% have oats. Overall, 83% have both chocolate chips or oats. What's the probability I find the kind of cookie recipe I want?

    Answers:

    • 54%

    • 19%

    • 18%

    • 23%

  • 26.

    In the marching band, 68% are flute players while seniors make up 40% of the band. Looking at a random member, there is a 70% chance that they are a flute player OR a senior, or both. What percent of the band both play the flute AND are seniors?

    Answers:

    • 28%

    • 108%

    • 42%

    • 38%

  • 27.

    A deck of playing cards has 52 total cards. Out of these 52 cards, 50% are red, while 7.6% are kings. Additionally, 53.8% of cards are red, OR a king, or both. What percent are red AND king?

    Answers:

    • 5.8%

    • 7.8%

    • 42.4%

    • 3.8%

  • 28.

    During a game where you roll a fair six-sided die, the probability of rolling an even value is 50%, while the probability of rolling a value larger than 4 is 33.3%. Overall, the probability of an even value OR a value larger than 4 (or both) is 66.7%. What is the probability of rolling a value that is even AND larger than 4?

    Answers:

    • 50%

    • 16.6%

    • 100%

    • 83.4%

  • 29.

    During rush hour, the highway gets really backed up at traffic lights. On one mile of the highway, there are two lights. For a random driver, the probability of stopping at the first light is 60%, while the probability of stopping at the second light is 80%. The probability of stopping at one light OR the other (or both) is 99%. What is the probability a driver has to stop at the first light AND the second light?

    Answers:

    • 140%

    • 48%

    • 41%

    • 19%

  • 30.

    A certain apartment complex has options for style and location. 59% of the apartments have blue paint while 20% have a view of the pool. Altogether, 72% have blue paint or a view of the pool (or both). What is the probability an apartment has blue paint AND a view of the pool?

    Answers:

    • 52%

    • 39%

    • 7%

    • 19%

Support