Mathematics: Abinomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experime n=10, p=0.4.X=4P(4)=(Do not round unul the final answer. Then round to four decimal places as needed.)

False similar are not exact congruent are the exact same ...

Abinomial probability experiment is conducted

casie65

29.01.2022

The probability of exactly '4' success

P( X=4) = 0.2508

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 10

Given probability of success 'p' = 0.4

q = 1 -p = 1 - 0.4 = 0.6

Step(ii):-

Let 'X' be the successes in binomial distribution

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

The probability of exactly '4' success

$P( x = 4) = 10_{C_{4} } (0.4)^{4} (0.6)^{10-4}$

we will use factorial notation

$10C_{4} = \frac{10!}{(10-4)!4!} = \frac{10 X 9 X 8 X 7 X6!}{6! 4!} = \frac{10 X 9 X8 X7}{4X 3X 2X1} = 210$

P( x = 4) = 210 X 0.0256 X0.0466

P( X=4) = 0.2508

conclusion:-

The probability of exactly '4' success

P( X=4) = 0.2508

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