(3 points) The probability of getting heads from throwing a fair coin is 1/2. Th
ID: 3049610 • Letter: #
Question
(3 points) The probability of getting heads from throwing a fair coin is 1/2. The fair coin is tossed 4 times. What is the probability that exactly 3 heads occur? 1/4 The fair coin is tossed 4 times. What is the probability that exactly 3 heads occur given that the first outcome was a head? 3/8 The fair coin is tossed 4 times. What is the probability that exactly 3 heads occur given that the first outcome was a tail? 1/8 The fair coin is tossed 4 times. What is the probability that exactly 3 heads occur given that the first two outcomes were heads? 1/2 The fair coin is tossed 4 times. What is the probability that exactly 3 heads occur given that there is at least 1 head? 4/15 A coin is rigged so that the probability of heads is 6/7 The rigged coin is tossed 4 times. What is the probability that exactly 3 heads occur? 864/2401 The rigged coin is tossed 4 times. What is the probability that exactly 3 heads occur given that the first outcome was a head? 10A The rigged coin is tossed 4 times. What is the probability that exactly 3 heads occur given that the first outcome was a tail? 21 143 The rigged coin is tossed 4 times. What is the probability that exactly 3 heads occur given that the first two outcomes were heads? 12/49 The rigged coin is tossed 4 times. What is the probability that exactly 3 heads occur given that there is at least 1 head?Explanation / Answer
Solution:
given a rigged coin,
probability of heads = p = 6 / 7 = 0.8571
binomial probability distribution
Formula:
P(k out of n )= n!*pk * qn-k / k! *(n - k)!
Probability that there are atleast 1 head = 1 - P( x < 1)
= 1 - 4!*0.85710 * 0.14294-0 / 0! *(4 - 0)!
= 1 - 0.0004
= 0.9996
probability that there will be exactly one 3 heads = 4!*0.85713 * 0.14294-3 / 3! *(4 - 3)!
= 0.3599
probability that exactly 3 heads occur given that there are atleast 1 head = 0.3599 /0.9996 = 0.3600
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