Question

Find the probability of exactly k successes in n repeated Bernoulli trials where the probability of success is p. (Round your answer to six decimal places.)

n = 7, k = 2, p = 0.4

Answer 1

Solution

Given that ,

p = 0.4

1 - p = 1 - 0.4 = 0.6

n = 7

K = 2

Using binomial probability formula ,

P(K = k) = ((n! / k! (n - k)!) * p^k * (1 - p)^{n - k}

P(K = 2) = ((7! /2 ! (7 - 2)!) * 0.4² * (0.6)^{7 - 2}

=  ((7! / 2! (5)!) * 0.4² * (0.6)⁵

= 0.261274

Probability = 0.261274