Math Data Management

Question

A baseball player has a batting average of 0.242. Find the probability that the player will get 4 hits in her next 34 at bats.

Answer 1

Probability of at least 4 hits = 1 - Probability of 0,1,2 or 3 hits

1-P(<4) = 1 - (P(0) + P(1) + P(2) + P(3))

1-Pr(<4) = 1- [34C0(.758)^34 + 34C1(.758)^33(.242) + 34C2(.758)^32(.242)^2 + 34C3(.758)^31(.242)^3]

nCr = n!/(n-r)!r! 34C0 = 1, 34C1 = 34, 34C2 = 34!/32!2! = 17(33)= 561, 34C3 = 34!/31!3! = 17(11)32=5984

but maybe you meant probability of exactly 4 hits, not any more or less than 4, then

P(4) = 34C4(.758)^30(.242)^4 = 34!/30!4!(.758)^30(.242)^4 = [34(33)(32)(31)/4(3)(2)](.758)^30(.242)^4

P(4) = 17(11)(8)(31)(.758)^30(.242)^4

P(4) = 46376(.758)^30(.242)^4

P(4) = 11.38595482(.242)^4

P(4) = 0.039050888

P(exactly 4 hits in 32 at bats) = about 3.91%