Maharashtra State BoardHSC Arts 12th Board Exam
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Choose the correct option from the given alternatives: If X ~ B(4, p) and P(X = 0) = 1681, the P(X = 4) = - Mathematics and Statistics

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MCQ

Choose the correct option from the given alternatives:

If X ~ B(4, p) and P(X = 0) = `16/81`, the P(X = 4) = ______

Options

  • `1/16`

  • \[\frac{1}{81}\]

  • \[\frac{1}{27}\]

  • \[\frac{1}{8}\]

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Solution

\[\frac{1}{81}\]

Hint:

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`

Concept: Binomial Distribution
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 8 Binomial Distribution
Miscellaneous exercise 8 | Q 5 | Page 253
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