Question

A die is thrown nine times. If getting an odd number is considered as a success, then the probability of three successes is ______

Options

• `""^9"C"_3(1/2)^7`

• `""^9"C"_6(1/2)^9`

• `""^9"C"_3(1/2)^8`

• None of these

Answer 1

A die is thrown nine times. If getting an odd number is considered as a success, then the probability of three successes is `underline(""^9"C"_6(1/2)^9)`.

Explanation:

Probability of getting an odd number is p = `3/6 = 1/2`

∴ q = `1 - 1/2 = 1/2`

Also, n = 9

∴ Required probability = P(X = 3)

= `""^9"C"_3(1/2)^3(1/2)^6 = ""^9"C"_3(1/2)^9`

= `""^9"C"_6(1/2)^9` .....`[∵ ""^"n""C"_"r" = ""^"n""C"_{"n" - "r"}]`