What is the probability of finding exactly five 7s in a given line?

Question

p = 0.1 and each line has 50 slots

 

Answer 1

Let random variable X be the number of 7s in a line of 50 slots.

 

The probability of getting exactly k successes in n trials is given by

P(X = k) = C(n, k) p^k(1-p)^n-k

 

For this problem

n = 50

k = 5

p = 0.1

 

So the probability of finding exactly five 7s in a line with 50 slots is

P(X = 5) = C(50, 5) (0.1)⁵(1-0.1)⁴⁵

             = 0.1849