Consider 10 independent tosses of a biased coin with the probability of Heads at each toss equal to p , where 0<p<1.

Question

Given that there were 4 Heads in the first 7 tosses, find the probability that the 2nd Heads occurred at the 4th toss. Give a numerical answer.

We are interested in calculating the probability that there are 5 Heads in the first 6 tosses and 3 Heads in the last 5 tosses. Give the exact numerical values of a,b,c,d that would match the answer ap7(1-p)3+bpc(1-p)d.

Thanks !!