A recent survey of rock bands by Rolling Stone reveals that 40% of rock & roll m

Question

A recent survey of rock bands by Rolling Stone reveals that 40% of rock & roll musicians have long hair. It's also true that 25% of rock & roll musicians are drummers. Furthermore, fun fact, it turns out that exactly half of rock drummers have long hair.

You go backstage to visit with "The Dry Martinis," the opening band for U2, whom you know nothing about (other than that they suck.) A long-haired man greets you at the door and says, "hello there, I'm a member of The Dry Martinis."

What's the probability that this guy is the drummer?

Explanation / Answer

Let the total number of musicians be 100

No. of musicians with long hair n(A)= 40% of 100= 40

No. of musicians who are drummers n(B)= 25% of 100= 25

Given, 1/2 of rock drummers has long hairs n(C)= 1/2 of 25=12.5

Required probablity i.e. musician with long hair is drummer = rock drummers with long hairs/musicians with long hair

=n(C)/n(A)= 12.5/40 = 5/16= 0.3125

Hence, the required probability is 0.3125

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