Question

I have a fair coin and a weighted coin that lands heads 60% of the time. I grab a coin at random. I flip that coin 5 times and get heads 4 times and tails once.

What is the probability that the coin I grabbed was the weighted coin? (answer to 3 decimal places)

Answer #1

Binomial distribution, P(X) = nCx p^{x}
q^{n-x}

P(getting 4 heads and 1 tail with fair coin) = 5C4 x
0.5^{4} x 0.5

= 0.15625

P(getting 4 heads and 1 tail with weighted coin) = 5C4 x
0.6^{4} x 0.4

= 0.2592

Bayes' Theorem: P(A | B) = P(A & B) / P(B)

P(weighted coin | 4 heads and 1 tail) = P(selecting weighted coin and getting 4 heads and 1 tail) / [P(selecting weighted coin and getting 4 heads and 1 tail) + P(selecting weighted coin and getting 4 heads and 1 tail)]

= (0.5 x 0.2592) / [(0.5 x 0.2592) + (0.5 x 0.15625)]

= **0.6239**

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