Question

Suppose that the probability of a baseball player getting a hit in an at-bat is 0.2804. If the player has 33 at-bats during a week, what's the probability that he gets no more than 9 hits?

Question 6 options: 1) 0.0768 2) 0.1536 3) 0.5493 4) 0.4507 5) 0.3957

Answer 1

X ~ Binomial (n,p)

P(X) = ⁿC_x p^x (1-p)^n-x

P( X <= 9) = P( X = 0) + P( X = 1) + P( X = 2) + P( X = 3) + P( X = 4) + P( X = 5) + P( X = 6) + P( X = 7) +

P( X = 8) + P( X = 9)

=  ³³C₀ 0.2804⁰ 0.7196³³ + ³³C₁ 0.2804¹ 0.7196³² + ³³C₂ 0.2804² 0.7196³¹ + ³³C₃ 0.2804³ 0.7196³⁰ +

³³C₄ 0.2804⁴ 0.7196²⁹ + ³³C₅ 0.2804⁵ 0.7196²⁸ + ³³C₆ 0.2804⁶ 0.7196²⁷ + ³³C₇ 0.2804⁷ 0.7196²⁶ +

³³C₈ 0.2804⁸ 0.7196²⁵ + ³³C₉ 0.2804⁹ 0.7196²⁴  

= 0.5493