Question

The probability that a randomly-selected person at a show has seen the band play live before is 50%. A "superfan" is defined as someone who has seen the band play live at least 5 times. The probability that a person at a show is a "superfan" is 30%. Two people are selected at random. What is the probability that both people have both seen the band perform live before, and are "superfans?"

Answer 1

Answer:

0.25 and 0.09

Step-by-step explanation:

The probability that a randomly-selected person at a show has seen the band play live before is 50%=0.50

The probability that a person at a show is a "superfan" is 30%=0.30

Two people are selected at random.

The probability that both people have both seen the band perform live before

= The probability that the first person has seen the band live before and the second person also has seen the band live before.

=0.50 x 0.50

=0.25

Similarly, the probability that both are  "superfans"

=The probability that the first person is a superfan and the probability that the second person is a superfan.

=0.30 x 0.30

=0.09

Hence, the probability that both people have both seen the band perform live before, and are "superfans" are 0.25 and 0.09 respectively.