Question

The average rate of scoring in baseball game is 0.5 run per inning.                                                                                                              

(a) What is the probability that not more than 2 runs will be scored in an inning? Just 1 run?                                                                                                 

(b) What is the probability that not more than 5 runs will be scored in the entire game? There are 9 innings in a game.       

Answer 1

a)

Here, λ = 0.5 and x = 2
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X > 2) = 1 - P(X <= 2).
P(X > 2) = 1 - (0.5^0 * e^-0.5/0!) + (0.5^1 * e^-0.5/1!) + (0.5^2 * e^-0.5/2!)
P(X > 2) = 1 - (0.6065 + 0.3033 + 0.0758)
P(X > 2) = 1 - 0.9856 = 0.0144

Here, λ = 0.5 and x = 1
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X = 1)
P(X = 1) = 0.5^1 * e^-0.5/1!
P(X = 1) = 0.3033
Ans: 0.3033

b)
Here, λ = 4.5 and x = 5
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X > 5) = 1 - P(X <= 5).
P(X > 5) = 1 - (4.5^0 * e^-4.5/0!) + (4.5^1 * e^-4.5/1!) + (4.5^2 * e^-4.5/2!) + (4.5^3 * e^-4.5/3!) + (4.5^4 * e^-4.5/4!) + (4.5^5 * e^-4.5/5!)
P(X > 5) = 1 - (0.0111 + 0.05 + 0.1125 + 0.1687 + 0.1898 + 0.1708)
P(X > 5) = 1 - 0.7029 = 0.2971