Question

The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is ______.

Options

• `""^5"C"_4 (0.7)^4 (0.3)`

• `""^5"C"_1 (0.7) (0.3)^4`

• `""^5"C"_4 (0.7) (0.3)^4`

• `(0.7)^4 (0.3)`

Answer 1

The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is `""^5"C"_4 (0.7)^4 (0.3)`.

Explanation:

Given that: `bar"P"` = 0.3

∴ p = 0.7 and q = 1 – 0.7 = 0.3

n = 5 and r = 4

We know that

P(X = r) = `""^"n""C"_"r" ("p")^"r".("q")^("n" - "r")`

∴ P(x = 4) = `""^5"C"_4 (0.7)^4 (0.3)^(5 - 4)`

= `""^5"C"_4 (0.7)^4 (0.3)`