# 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?

• 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?

• 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?

• 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?

• 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?

• 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?

• 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 _____.

• 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?

• 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?

• 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?

• 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 ?

• 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?

• 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?

• 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?

• 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?

• 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?

• 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)

• 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?

• 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?

• 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?

• 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?

• 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?

• 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?

• 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?

• 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?

• 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?

• 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?

• 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?

• 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?

• 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?