Pavukol

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:
$\left(\genfrac{}{}{0}{}{60}{20}\right)$ $\ast {0.5}^{20}\ast \left(1-.5{\right)}^{40}$

Do you have a similar question?

cerfweddrq

Expert

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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