Question

For a binomial probability function with P=0.4 and n=17, find the probability that the number of successes is equal to 9 and the probability that the number of successes is fewer than 8.

​P(9​ successes)=____

Answer 1

Solution

Given that ,

p = 0.4

1 - p = 1 - 0.4 = 0.6

n = 17

x = 9

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * p^x * (1 - p)^{n - x}

P(X = 9) = ((17! / 9! (17 - 9)!) * 0.4⁹ * (0.6)^{17 - 9}

=   ((17! / 9! (8)!) * 0.4⁹ * (0.6)⁸

=  0.1070

P(9 successes) = 0.1070

P(x < 8) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4) + P(x = 5) + P(x = 6) + P(x = 7)

P(x < 8) = 0.6405

The probability that the number of successes is fewer than 8 is 0.6405