There are 30 balls numbered 1-30 in a bag. One is randomly selected 12 times. What is the probability of getting a prime number exactly five times?

The probability of getting a prime number exactly five times = 0.1908

Step-by-step explanation:

Prime numbers from 1 to 30 are 2,3,5,7,11, 13, 17, 19, 23, 29.

The probability of getting a prime number p=

Number of trials n = 12

Binomial probability formula:

, where x= number of successes

n= number of trials.

x = Number of successes

p= probability of getting one success.

The probability of getting a prime number exactly five times:

Hence, the probability of getting a prime number exactly five times = 0.1908