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)prqn−r
In this case, the probability of success is p=0.10 and the probability of failure q=1−p=0.90.
a.) The probability that exactly 12 out of 15 are left-handed is
=C(15,12)(0.10)12(0.90)15−12
=C(15,12)(0.10)12(0.90)3
=3.3117×10−10
b.) The probability that 12 or more left-handed are selected is equal to
=C(15,12)(0.10)12(0.90)15−12+C(15,13)(0.10)13(0.90)15−13+C(15,14)(0.10)14(0.90)15−14+C(15,15)(0.10)15(0.90)15−15
=3.317×10−10+8.505×10−12+1.35×10−13+1×10−15
=3.403×10−10
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