Question:

A biased coin is flipped 10 times. (The probability of rolling a heads is p.)

Given that 6 heads result, what is the conditional probability that the first 3 outcomes are heads,tails,tails.

What I have so far::

let A = event that you roll heads,tails,tails in your first three rolls of 10 total rolls
let B = event that you roll 6 heads out of 10 total rolls

P(A given B) = P(A intersect B) / P(B)

P(B) = C(10,6)(p^6)(1-p)^4
P(A intersect B) = C(7,5)(p^5)(1-p)^2

My problem::
The solution is given as an explicit value not containing p. My answer of P(A intersect B)/P(B) contains the value p. Is there some way to calculate p? Or perhaps my logic is incorrect

Thank you