Question

Illinois license plates used to consist of either three letters followed by three digits or two letters followed by four digits. Assume that all the different possible license plates are equally likely.

(a) What is the probability that a randomly chosen plate contains the number 4444? (Round your answer to six decimal places.)


(b) What is the probability that a randomly chosen plate contains the substring BE? (For example, BE4321 or PBE786 are two ways BE might appear. Round your answer to six decimal places.)

Answer 1

The number of ways in which the license plate will have three letters followed by three digits = X = 26*26*26*10*10*10

The number of ways in which the license plate will have two letters followed by four digits = Y = 26*26*10*10*10*10

Total number of possibilities = X + Y = 24336*1000

Ans a:

Number of ways that a plate contains the number 4444 = 26*26*1*1*1*1

probability = 26*26/24336000 = 0.000028

Ans b:

Number of ways that a plate contains the substring BE = 10*10*10*10 + 26*10*10*10 + 26*10*10*10 = 62*1000

probability = 62*1000/24336000 = 0.002548