Question

Rn a has 14 white and 7 red balls. urn b has 2 white and 13 red balls. we flip a fair coin. if the outcome is heads, then a ball from urn a is selected, whereas if the outcome is tails, then a ball from urn b is selected. suppose that a white ball is selected. what is the probability that the coin landed heads?

Answer 1

$p(H)=p(T)=1/2\]\[p(W/H)=14/21 , \p(W/T)=2/15\]\[p(W)=p(H)p(W/H)+p(T)p(W/T)=2/5\]\[p(H/W)=p(H)p(W/H)/p(W)=5/6$