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

Question

1. Let A be the event that there are 6 Heads in the first 8 tosses. Let B be the event that the 9th toss results in Heads.

Find P(B∣A) and express it in terms of p using standard notation. (You can click on the “STANDARD NOTATION" button below.)

2. Find the probability that there are 3 Heads in the first 4 tosses and 2 Heads in the last 3 tosses. Express your answer in terms of p using standard notation. Remember not to use ! or combinations in your answer.

3. 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.

4. 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.
a=
b=
c=
d=

Answer 1

1. = p
2. = 12*p^5*(1-p)^2
3. = 9/35
4.a =
4.b =
4.c =
4.d =

Can someone find the 4.a, 4.b, 4.c, 4.d? :)

Answer 2

4.c = 8

Answer 3

4.b = 4
4.c = 8

Answer 4

4.a =30
4.b =4
4.c =8
4.d =2