# 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

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

• $\frac{1}{81}$

• $\frac{1}{27}$

• $\frac{1}{8}$

#### 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