# Choose the correct option from the given alternatives: The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probablity of 2 successes is - Mathematics and Statistics

MCQ

Choose the correct option from the given alternatives:

The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

#### Options

• 128/256

• 219/256

• 37/256

• 28/256

#### Solution

28/256

Explanation:

np = 4, npq = 2

∴ q = 1/2 and p = 1/2

∴ "n"(1/2) = 4

∴ n = 8

∴ P(X = 2) = "^8C_2 (1/2)^8 = (8 xx 7)/(1 xx 2) xx 1/256 = 28/256

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 2 | Page 253