Consider 10 independent tosses of a biased coin with the probability of Heads at each toss equal to p, where 0 < p < 1. (a) Let A be the event that there are exactly 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. (b) Find the probability that there are exactly 3 Heads in the first 4 tosses and exactly 2 Heads in the last 3 tosses. Express your answer in terms of p.
Consider 10 independent tosses of a biased coin with the probability of Heads at each toss equal to p, where 0 < p < 1. (a) Let A be the event that there are exactly 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. (b) Find the probability that there are exactly 3 Heads in the first 4 tosses and exactly 2 Heads in the last 3 tosses. Express your answer in terms of p.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Transcribed Image Text:Consider 10 independent tosses of a biased coin with the probability of Heads at each toss
equal to p, where 0 < p < 1.
(a) Let A be the event that there are exactly 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.
(b) Find the probability that there are exactly 3 Heads in the first 4 tosses and exactly
2 Heads in the last 3 tosses. Express your answer in terms of p.
(c) Given that there were exactly 4 Heads in the first 7 tosses, find the probability that
the 2nd Heads occurred at the 4th toss. Give a numerical answer.
(d) Find the probability that there are exactly 5 Heads in the first 8 tosses and exactly
3 Heads in the last 5 tosses.
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VIEWStep 2: Find the probability P(B|A):
VIEWStep 3: Find the probability that exactly 3 Heads in 1st 4 tosses and exactly 2 Heads in last 3 tosses:
VIEWStep 4: Find the probability the 2nd Heads occurred at the 4th toss:
VIEWStep 5: Find the probability that exactly 5 Heads in 1st 8 tosses & exactly 3 Heads in last 5 tosses:
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