examday

/TMUA

Coins $A$ and $B$ have probabilities $p$ and $q$ of landing heads, respectively, where $0<q<p<1$. All tosses are independent.

It is given that $p+q=13/12$. When each coin is tossed once, the probability that both land heads is $1/4$.

Coin $A$ is now tossed twice and coin $B$ once. Given that exactly two of these three tosses land heads, what is the probability that coin $B$ lands tails?