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Question 617935: Suppose we want to determine the (binomial) probability(p) of getting 5 heads in 11 flips of a 2-sided coin. Using the Binomial Probabilities Table in Appendix B of the text, what values of n, x and p would we use to look up this probability, and what would be the probability?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the value of n would be 11
the value of x would be 5
the value of p would be .5
the value of q = 1-p would also be .5
the formula is:
nCx*p^x*q^(n-x)
you should get:
11C5*.5^5*.5^6 equals .225585938
11C5 is equivalent to 11! / (5!*6!) which is equal to 462
.5^5 is equal to .03125
.5^6 is equal to .015625
all of the probabilities are shown in the following table.
the sum of the probabilities should be equal to 1 as shown.
n x nCx (.5)^x (.5)^(n-x) nCx*(.5)^x*(.5)^(n-x)
11 0 1 1 0.000488281 0.000488281
11 1 11 0.5 0.000976563 0.005371094
11 2 55 0.25 0.001953125 0.026855469
11 3 165 0.125 0.00390625 0.080566406
11 4 330 0.0625 0.0078125 0.161132813
11 5 462 0.03125 0.015625 0.225585938 *****
11 6 462 0.015625 0.03125 0.225585938
11 7 330 0.0078125 0.0625 0.161132813
11 8 165 0.00390625 0.125 0.080566406
11 9 55 0.001953125 0.25 0.026855469
11 10 11 0.000976563 0.5 0.005371094
11 11 1 0.000488281 1 0.000488281
total probability >>>>> 1
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