Suppose Player A and Player B are flipping a coin. Player A flips the coin 20 times, and Player B 40 times. What would be the probability that Player A gets 10 heads from his 20 flips, given that 20 heads were found in total.
I know we can use the binomial distribution to find the denominator(20 heads in 60 flips), but I'm wondering what exactly would b in the numerator. Would I use the binomial distribution as well?
This is my denominator:
Answer & Explanation
Trusting that you mean "exactly" in each instance (so "exactly" 20 heads tossed, etc.) then the numerator is the joint probability that A throws exactly 10 Heads AND B throws exactly 10.
By independence, this joint probability is just a product and the two factors can easily be computed from the binomial distribution.
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