Venn diagrams for probability Problem set A

Of 50 families, 30 have a dog and 20 have a cat. 8 families have both. One family is chosen at random. Find the probability that the family has

1. (a) a dog but not a cat.
2. (b) a cat but not a dog.

In a class of 36 students, 22 play football and 15 play hockey. 7 play both. Find the probability that a student chosen at random plays neither sport.

The Venn diagram shows the 60 members of a gym. C is the set who attend classes and W is the set who use the weights room. The numbers are numbers of members. A member is chosen at random. Find the probability that the member

1. (a) attends classes.
2. (b) attends classes but does not use the weights room.
3. (c) is in neither set.

In a school of 90 students, 14 study both French and Spanish, 20 study neither language and 33 study French only.

1. (a) How many students study Spanish only?
2. (b) A student is chosen at random. Find the probability that the student studies Spanish.

A survey asks 120 people what they watch. 70 watch drama, 55 watch comedy and 25 watch both.

1. (a) Draw a Venn diagram.
2. (b) Find the probability that a person chosen at random does neither.
3. (c) Find the probability that a person chosen at random does exactly one.

Of 200 shoppers, 36 buy both bread and milk, 24 buy neither and 75 buy milk only. A shopper is chosen at random. Find the probability that the shopper buys bread. Give your answer as a decimal.

In a village, the probability that a house has broadband is 0.6 and the probability that it has a landline is 0.5. The probability that it has neither is 0.1.

1. (a) Find the probability of a house having both.
2. (b) Find the probability of a house having broadband but no landline.

In a club of 80 members, 20 do both kayaking and climbing and 12 do neither. The number who do kayaking only is 8 more than the number who do climbing only. Find the probability that a member chosen at random does climbing. Give your answer as a fraction.