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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)`
Solution
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)`
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