Question:
A die is thrown 5 times. Find the probability that an odd number will come up exactly three times.
Solution:
Here, p = 1/6 + 1/6 + 1/6 = ½ ⇒ q = 1 – ½ = ½ and n = 5
Now,
P(x = r) = nCr pr qn – 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.