The following table has information on the number of cars that pass through a ce

Question

The following table has information on the number of cars that pass through a certain intersection between 2:00PM and 2:05PM, and the probability for each number of car:

Cars 0 1 2 3 4 5

Prob 0.36 0.28 0.15 0.10 0.07 0.04

I.e, the probability that 0 cars pass through is 0.36, etc.

a) Find the probability at least one car passes through the intersection between the specified times.

b) Find the probability that between 2 and 4 cars (inclusive) pass through the intersection between the specified times.

c) Find the probability that no cars pass through the intersection between the specified times.

d) Find the probability an even number of cars pass through the intersection between the specified times.   

Explanation / Answer

Part a

Probability that atleast one car passes through the intersection = 1 - probability that no car passes through the intersection = 1- 0.36 = 0.64

Part b

Probability that between 2 and 4 cars (inclusive) pass through the intersection = probability of 2 car passing the intersection + probability of 3car passing the intersection + probability of 4 car passing the intersection + 0.15 + 0.1 + 0.07 = 0.32

Part c

Probability that no car passes through the intersection = 0.36

Part d

Probability that an even number of cars pass through the intersection = probability of 2 cars passing + probability of 4 cars passing = 0.15 + 0.07 = 0.22

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