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Question
If X ~ B(4, p) and P(X = 0) = `16/81`, then P(X = 4) = ______.
Options
`1/16`
\[\frac{1}{81}\]
\[\frac{1}{27}\]
\[\frac{1}{8}\]
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Solution
If X ~ B(4, p) and P(X = 0) = `16/81`, then P(X = 4) = `underlinebb(1/81)`.
Explanation:
P(X = 0) = `"^4C_0 p^0 q^4 = 16/81`
∴ `"q"^4 = (2/3)^4`
∴ q = `2/3`
∴ p = 1 – q = `1 - 2/3 = 1/3`
∴ P(X = 4) = `"^4C_4 p^4 q^0 = (1/3)^4 = 1/81`
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