williamrobertsuk
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 May 18, 2019
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Consider 10 independent tosses of a biased coin with the probability of Heads at each toss equal to p, where 0<p<1.
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.
=p
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.
=12*p^5*(1p)^2
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.
=9/35
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=
I have managed to find the answers for the questions 1, 2, 3 but number 4 tricks me a bit, someone that can help? I attached a screenshot of question 4 too. Thanks!
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.
=p
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.
=12*p^5*(1p)^2
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.
=9/35
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=
I have managed to find the answers for the questions 1, 2, 3 but number 4 tricks me a bit, someone that can help? I attached a screenshot of question 4 too. Thanks!
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