Question

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

Answer 1

Here, p = `1/6 + 1/6 + 1/6 = 1/2`

q = `1 - 1/2 = 1/2`

And n = 5

∴ P(x = r) = `""^"n""C"_"r" "p"^"r" "q"^("n" - "r")`

= `""^5"C"_3 (1/3)^3 (1/2)^(5-3)`

= `(5!)/(3!2!) * (1/2)^3 * (1/2)^2`

= `10*1/8*1/4`

= `5/16`

Hence, the required probability is `5/16`.