Question

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?

Answer 1

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

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=
`(10)/(30)=\frac13`

Number of trials n = 12

Binomial probability formula:

`P(X=x) = \ ^nC_x p^x(1-p)^(n-x)`

, 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:

`P(X=5)=\ ^(12)C_5(\frac13)^5(1-\frac13)^(7)`

`=(12!)/(5!7!)(\frac1{243})((128)/(2187))\\\\=0.1908`

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