Monday, July 15, 2019

College Algebra, Chapter 10, 10.4, Section 10.4, Problem 20

A psychologists needs 12 left-handed subjects for an experiment, adn she interviews 15 potential subjects. About 10% of the population is left-handed.

a.) What is the probability that exactly 12 of the potential subjects are left-handed?

b.) What is the probability that 12 or more are left-handed?

Recall that the formula for the binomial probability is given by

C(n,r)prqnr

In this case, the probability of success is p=0.10 and the probability of failure q=1p=0.90.

a.) The probability that exactly 12 out of 15 are left-handed is

=C(15,12)(0.10)12(0.90)1512

=C(15,12)(0.10)12(0.90)3

=3.3117×1010

b.) The probability that 12 or more left-handed are selected is equal to

=C(15,12)(0.10)12(0.90)1512+C(15,13)(0.10)13(0.90)1513+C(15,14)(0.10)14(0.90)1514+C(15,15)(0.10)15(0.90)1515

=3.317×1010+8.505×1012+1.35×1013+1×1015

=3.403×1010

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