Question

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=4
P(4)=
(Do not round unul the final answer. Then round to four decimal places as needed.)​

Answer 1

Answer:

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