Answer to Question #261698 in Statistics and Probability for A.A

Question

suppose we have two hats one has 4 red balls and 6 green balls, the other has 6 red and 4 green. we toss a fair coin, if heads, pick a random ball from the first hat, if tails from the second. What is the probability of getting a red ball.

Answer 1

Solution:

$P(Red)=P(Red|H).P(H)+P(Red|T).P(T) \\=\dfrac{4}{10}.\dfrac{1}{2}+\dfrac{6}{10}.\dfrac{1}{2} \\=\dfrac{1}{2}$