Could I get an explanation for this question?

Question

A high school baseball player has a 0.167 batting average. In one game, he gets 9 at bats. What is the probability he will get at least 5 hits in the game?

Answer 1

9 at bats, P(hit) = .167 = 167% of a hit at each at bat

expected number of hits after 9 at bats = 9x.167 = 15.03

P(5 or more) = .167^5(.833^4) + .167^6(.833^3) + .167^7(.833^2) + .167^8(.833) + .167

use a calculator

= about .0000781974264

= about .008% chance of 5 hits or more

expected # of hits in 9 at bats is about 1 or 2

Answer 2

Use binomial distribution formula:

probability x successes in n tries where probability of success for each try is p:

x n-x

n! p (1-p)

------

x! (n-x)!

Here n = 9, p = 0.167. determine probability when x = 5, 6, 7, 8 and 9, using the above formula.

Add those probabilities together