00:01
Here on this problem, we are told that the distribution of the number of cars per year that will experience a catastrophe is plus on with lambda being equal to 5.
00:09
And so what this would mean is that the probability of x is e to the negative fifth times 5 to the x over x factorial.
00:20
Now in a, we want to find the probability that at most three cars per year will experience our catastrophe.
00:26
And so we want the probability that x is less than re -equal to three.
00:31
This is equal to the sum of x being 0 through 3 of e to the negative 5th times 5 to the x over x factorial.
00:44
This just means that we're finding the probability of 0, 1, 2, and 3, and then adding them all together.
00:54
And so we take e to the negative 5 times 5 to the x over x factorial, and you can either type this in in a calculator or plug in 0, 1, 2, and 3, and add them all together.
01:04
When we do, this gives us 0 .2650...