Question

Rogers Hornsby has a lifetime batting average of 0.358. Assume that Rogers Hornsby came to bat officially six times every game played. What would be Rogers Hornsby's probability getting at least five hits in a game?

Answer 1

here we have,

proportion, p = 0.358

sample size, n = 6

we know that,

P(X = x) = ⁿC_x p^x (1-p)^n-x

Probability of getting at least five hits is,

P(x >=5) = P(X = 5) + P(X = 6)

= 6C5 * 0.358^5 * (1-0.358)^(6-5) + 6C6 * 0.358^6 * (1-0.358)^(6-6)

= 0.02265 + 0.00211

= 0.0248 (Rounded to 4 decimal places)

please revert if any doubts