Statistic probability distribution

Question

A baseball player has a batting average of 0.335. what is the probability that he has exactly 4 hits in his next 7 at bats? Round answer to four decimal places.

Answer 1

This is a case of binomial distribution. The player either hits or does not hit.

Use binomial probability formula

P(x successes in n tries) = C(n, x)p^x(1–p)^n–x

P(x successes in n tries) = n!

[p^x (1-p)^ (n-x)]

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x! (n-x)!

where p = probability of success

here p = 0.335, n = 7 and x = 4

The first part = (7x6x5x4x3x2x1) / [ (4x3x2x1) x (3x2x1) = FACT(7) / [ FACT(4) x FACT(3) ] = 35

P(4 successes in 7 tries) = 35 x POWER(0.335,4) x (POWER(1-0.335),3))

Or, P(4 successes in 7 tries) = 35 x POWER(0.335,4) x POWER(0.665,3)

Or, P(4 successes in 7 tries) = 35 x 0.0126 x 0.2941 = 0.1296 (up to 4 decimal places)

Answer = 0.1296 (up to 4 decimal places)