Sets 3

A group of 40 students is surveyed. 18 students play tennis (set T), and 6 students play both tennis (T) and basketball (B). What is the number of students who play both tennis and basketball, n(T ∩ B)?

In a club of 50 members, 32 members play chess (set C), 19 members play cards (set D), and 7 members play both chess and cards. Use set notation to calculate the number of members who play only chess.

Set A = {students who play guitar}, Set B = {students who play piano}, in a class of 28 students. Explain using set notation how you would find the number of students who play either guitar or piano, but not both.

In a survey of 60 people:

• 36 people like apples (A),

• 24 people like bananas (B),

• 12 people like both apples and bananas.

A person is chosen at random from the survey.

The Venn diagram below shows information about a class of 50 students and whether they have a pet cat (C) or a pet dog (D).

Let S = {students who play a musical instrument}, U = {all students in class}. Write, in set notation, the set of students who do not play a musical instrument.

In a class, n(A) = 18, n(B) = 12, and n(A ∩ B) = 5. Find n(A ∪ B).

In a survey of 60 students, 38 play football (F), and 15 play both football and tennis (T). A student is chosen at random. Calculate the probability that the student plays tennis given that they play football.

On a Venn diagram, set A represents people in a club who speak French, and set B represents those who speak Spanish. Out of 40 people, 18 speak French, 22 speak Spanish, and 9 speak both languages. Calculate how many people speak only Spanish.

Let and be sets in a universal set . Explain, using set notation, how to find the probability that an element chosen at random from lies in , and why you cannot simply add and unless and are disjoint.