Wednesday, June 19, 2019

College Algebra, Chapter 10, 10.4, Section 10.4, Problem 12

Five independent trials of a binomial experiment with probability of success p=0.7 and probability of failure q=0.3 are performed. Find the probability of each event.

At most two failures

Recall that the formula for the binomial probability is given by

C(n,r)prqnr

If the event should have at most two failures, then it means that the event must have at least three successes. Thus, we have


P(At least three successes)=P(exactly 3 successes)+P(exactly 4 successes)+P(exactly 5 successes)=C(5,3)(0.7)3(0.3)53+C(5,4)(0.7)4(0.3)54+C(5,5)(0.7)5(0.3)55=0.3087+0.36015+0.16807=0.83692

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