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saw5 [17]
3 years ago
6

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n indepe

ndent trials of the experiment.
n=10, p=0.5, x=4

p(4)

​(Do not round until the final answer. Then round to four decimal places as​ needed.)
Mathematics
1 answer:
Arlecino [84]3 years ago
3 0

Answer:

P(4) =p(x=4) = 0.205078

Step-by-step explanation:

<u>Explanation</u>:-

The probability of x successes in the n independent trials of the experiment.

Given n=10, p=0.5,

By using Binomial distribution

P(X =x) =  n_{C_{x} } p^{x} q^{n-x}

Given the p = 0.5

               q=1-p =1-0.5=0.5

P(X =4) =  10_{C_{4} } (0.5)^{4} (0.5)^{10-4}

we will use formula

n_{C_{r} } = \frac{n!}{(n-r)!r!}

10_{C_{4} } = \frac{10!}{(10-4)!4!}=\frac{10X9X8X7X6!}{6!4!} =\frac{10X9X8X7}{4X3X2X1} =210

P(X =4) =  210 (0.5)^{4} (0.5)^{10-4}

P(X =4) =  210 (0.5)^{4} (0.5)^{6}

on calculation, we get

P(X=4) = 0.205078

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