Given that there were 5 heads in 12 tosses of a fair coin. What is the probability that the last two tosses were heads?

Question

It's a binomial random variable type of problem, and I'm not sure how to start.

Answer 1

Let event A = 5 heads in 12 tosses

Let event B = last 2 of 12 tosses are heads

P(A) = $\left(\genfrac{}{}{0ex}{}{12}{5}\right)$ * (1/2)^12

P(B) = 2^10 / 2^12

P( A and B) = $\left(\genfrac{}{}{0ex}{}{10}{3}\right)$ * (1/2)^10 * 1/4

P(B|A) = P(A and B)/P(A) = $\left(\genfrac{}{}{0ex}{}{10}{3}\right)$ / $\left(\genfrac{}{}{0ex}{}{12}{5}\right)$ = 120/792 = .015152