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

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= $\dfrac{10}{30}=\dfrac13$

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:

$P(X=5)=\ ^{12}C_5(\frac13)^5(1-\frac13)^{7}$

$=\frac{12!}{5!7!}(\frac1{243})(\frac{128}{2187})\\\\=0.1908$

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