Pavukol

Pavukol

Answered

2022-09-11

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:
( 60 20 ) 0.5 20 ( 1 .5 ) 40

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Answer & Explanation

cerfweddrq

cerfweddrq

Expert

2022-09-12Added 15 answers

Step 1
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.
Step 2
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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