In a major league baseball game the average is 19 broken bat

In a major league baseball game, the average is 1.9 broken bat per game. (a) Find the probability of no broken bats in a game. Probability (b) Find the probability of at least 2 broken bats in a game. Probability

Solution

a)

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    1.9      
          
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.149568619 [ANSWER]

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b)

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    1.9      
          
x = our critical value of successes =    2      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   1   ) =    0.433748996
          
Thus, the probability of at least   2   successes is  
          
P(at least   2   ) =    0.566251004 [ANSWER]