Question

A football stadium has an attendance of

4993

people. Of​ these,

2105

are cheering for Team A and

2569

are female. Of the people cheering for Team​ A,

nine hundred and eight eight

are female. Find the probability that a randomly selected attendee is female or cheers for Team A.

​(a) Are the events​ "cheering for Team​ A" and​ "being a​ female" mutually​ exclusive?

yes or no?

b) what is the probability that a randomly selected attendee is female or cheers for team A?

___ (type an integer or decimal rounded 3 places if it is needed)

.8

Answer 1

a)

For the event that the selected attendee is female and selected attendee cheers for Team A to be mutually exclusive, there should be no attendee who is a female and cheers for Team A.

But there are 988 females and cheering for Team A.

Hence, No. The two given events are not mutually exclusive.

b)

Required probability = P(selected attendee is female or cheers for team A)

= P(selected attendee is female) + P(selected attendee cheers for team A) - P(selected attendee is female and cheers for team A)