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Find the probability of exactly four successes in five trials of a binomial experiment in which the probability of success is 40%. Round to the nearest tenth of a percent.

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sqdancefan

Answer:

p(4 successes) ≈ 7.7%

Step-by-step explanation:

p(k successes in n trials) = C(n,k)·p^k·(1-p)^(n-k)

You have n=5, k=4, p=0.4, so the probability is ...

p(4 successes) = C(5,4)·(0.4)^4·(1 -0.4)^1 = 5·0.4^4·0.6 = 0.0768

p(4 successes) ≈ 7.7%

Answer:

P(4 success)=0.0768

Step-by-step explanation:

The Probability for r success in binomial distribution is given by:

P(r success)=[tex]n_{C_{r}}p^rq^{n-r}[/tex]

Where n is the number of trails

p is the probability of success in each trial

q =1-p which is the probability of failure

Here r=4

n=5

p=40%=0.4 and q=1-0.4=0.6

Hence, P(4 success)= [tex]5_{C_{4}}0.4^40.6^{5-4}[/tex]

                                 =  [tex]5\times 0.4^4\times 0.6[/tex]

                                 = 0.0768

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