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Question
Choose the correct option from the given alternatives:
For a binomial distribution, n = 5. If P(X = 4) = P(X = 3), then p = ______
Options
`1/3`
`3/4`
1
`2/3`
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Solution
`2/3`
Explanation:
P(X = 4) = P(X = 3)
∴ `""^5C_4 p^4 q = "^5C_3 p^3 q^2`
∴ 5p = 10q
∴ 5p = 10(1 - p)
∴ p = `(10(1 - "p"))/5`
∴ p = 2 - 2p
∴ p + 2p = 2
∴ 3p = 2
∴ p = `2/3`
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= `square` + `square`
= `2/27`
