Lowe’s Interview Questions | Fair Coin

Question

You are given a biased coin (both sides heads) and a fair coin. You randomly pick one of then and toss it 5 times. The result comes out to be tails every time.

What is the probability that you picked a fair coin?

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Dhruv2301 55 years 2 Answers 1084 views Great Grand Master 0

Answers ( 2 )

  1. Ramya Mamidipaka
    1
    Reply

    If its always tails, then the probability of the coin being fair is 1.

    If its always head:
    p(fair|5 heads)
    =p(5 heads|fair)p(fair)/ p(5 heads)
    =p(5 heads|fair)p(fair)/(p(5 heads|fair)p(fair)+p(5 heads|unfair)p(unfair))
    =(1/2)^5*(1/2)/((1/2)^5*(1/2)+(1)^5*(1/2))
    =1/33

    Correct me if I am wrong

    0
    Reply

    we can use bayes rule here
    A: fair coin
    B: getting 5 tails

    find : P(A/B)=?

    P(B/A)=(1/2)^5 * (1/2)
    P(A)=1/2
    P(B)=(1/2)^5 * (1/2) + 0* 1/2
    P(A/B)=(P(B/A) * P(A))/ P(B)
    =(1/2)^5 * (1/2) / ((1/2)^5 * (1/2)
    =1

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