Suppose earthquakes occur in the western US with a rate of 2

Suppose earthquakes occur in the western US with a rate of 2 per week. Let X be the number of earthquakes in the western US this week. Let Y be the number of earthquakes in the western US this month (assume one month = 4 weeks). What is the probability Y=5?

Solution

As there are 2 per week, then there are 2*4 = 8 per 4 weeks.

Thus,

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 =    8      
          
x = the number of successes =    5      
          
Thus, the probability is          
          
P (    5   ) =    0.091603662 [ANSWER]