A high school baseball player has a 0.202 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

P(>4) = 1-P(<5)

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

=P(5)+P(6)+P(7)+P(8)+P(9)

=9C5(.202)^5(.798)^4 +9C6(.202)^6(.798)^3 +9C7(.202)^7(.798)^2+9C8(.202)^8(.798)+(.202)^9

=126(.0003363)(.4055) + ...

= about .017 + ...

(some very tedious calculations)

nCr= n!/r!(n-r)!

9C5=9!/5!4!=9x8x7x6/4x3x2=9x7x2=126

9C6=9!/6!3!=9x8x7/3x2=3x4x7=84

9C7=9!/7!2!=9x8/2=36

9C8=9!/8!=9

those coefficients are the 9th row of Pascal's Triangle

1,9,36,84,126, ...