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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?

User Noobular
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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

User GraphicalDot
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