Sets 3

In a group of 100 people, 65 like apples (A), 52 like bananas (B), and 29 like both apples and bananas.

54 children were surveyed about their favourite types of fruit. The Venn diagram below shows the number of children who like oranges (O), bananas (B), and apples (A).

Complete the table by finding the number of children who do not like any of these three fruits. Then, using the information, find the probability that a randomly selected child from this group likes at least two of the three fruits.

Let , , and the universal set . Write down the set and its number of elements.

In a set of 32 students, 18 study Physics (P), 15 study Chemistry (C), and 7 study both subjects. Work out the number of students who study either Physics or Chemistry, but not both.

A group of students was asked if they like music (M) and if they like art (A). Explain how you would use set notation and probability to work out the probability that a randomly selected student likes at least one of music or art, and the probability that a randomly selected student likes neither.

Out of 80 participants in a charity run, 48 ran the full course, 35 took part in the half course, and 18 ran both the full and half course.

What is the probability that a randomly selected participant ran at least one of the two courses?

In a group of 50 students:

In a club, every member either plays table tennis (T), badminton (B), or both. There are 60 members in total. 42 members play table tennis, 28 play badminton, and members play both.

Given that a member is chosen at random and is known to play table tennis, the probability that they also play badminton is .