Question

How many different license plates can be generated in a particular State where plates display 4 letters followed by 4 numbers, allowing for repetitions?

A) 456,976,000
B) 26,000,000
C) 1,679,616
D) 36,000,000

Answer 1

The number of different license plates that can be generated in the particular State is 456,976,000. Renate's chance of winning one of the licenses is approximately 0.00000909. G and F are independent events, and G and F are not mutually exclusive events.

Step-by-step explanation:

a. The number of possible outcomes (microstates) of any repeated independent situation is equal to the number of possibilities in one iteration to the power of the repetitions. So in this case, the answer is 26 (the number of letters) to the power of 4, multiplied by 10 (the number of digits) to the power of 4, which is equal to 456,976,000.

b. Since each finalist has an equal chance of winning, Renate's chance of winning one of the licenses is 1 divided by the total number of finalists, which is 1/110,000 or approximately 0.00000909.

c. G and F are independent events because the number of winners (G) is not affected by the number of finalists (F). The probability of G occurring is the same regardless of whether F occurs or not.

d. G and F are not mutually exclusive events because it is possible for Renate to be both a finalist and a winner. In fact, being a finalist increases her chances of winning.