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The probability that a randomly selected person at a show has seen the band play live before is 30%. A "superfan" is defined as someone who has seen the band play live at least 10 times. The probability that a person at a show is a "superfan" is 20%. Two people are selected at random. What is the probability that both people have both seen the band perform live before, and are superfans?

User Manan
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1 Answer

6 votes

Answer:

0.09 and 0.04

Explanation:

The probability that a randomly-selected person at a show has seen the band play live before is 30%=0.30

The probability that a person at a show is a "superfan" is 20%=0.20

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.

=0.30 x 0.30

=0.09

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.

=0.20 x 0.20

=0.04

Hence, the probability that both people have both seen the band perform live before, and are "superfans" are 0.09 and 0.04 respectively.

User T D Nguyen
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