A die is thrown 5 times. Find the probability that an odd number will

1.	A die is thrown 5 times. Find the probability that an odd number will come up exactly three times.
Answer» Here, p = 1/6 + 1/6 + 1/6 = ½ ⇒ q = 1 – ½ = ½ and n = 5 Now, P(x = r) = ⁿC_r p^r q^{n – r} = ⁵C₃ (1/2)³(1/2)^5-3 = [5!/(3!2!)].(1/2)³(1/2)² = 10.1/8.1/4 = 5/16 Therefore, the required probability is 5/16.

A die is thrown 5 times. Find the probability that an odd number will come up exactly three times.

Answer»

Here, p = 1/6 + 1/6 + 1/6 = ½ ⇒ q = 1 – ½ = ½ and n = 5

Now,

P(x = r) = ⁿC_r p^r q^{n – r} = ⁵C₃ (1/2)³(1/2)^5-3

= [5!/(3!2!)].(1/2)³(1/2)² = 10.1/8.1/4 = 5/16

Therefore, the required probability is 5/16.

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A die is thrown 5 times. Find the probability that an odd number will come up exactly three times.

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