Question

1.a) In a 12-question matching test with 12 possible answers to match and no answer used more than once, what is the probability of guessing and getting every answer correct? (Enter your probability as a fraction.)

b) Suppose that all license plates in a state have three letters and then four digits. If a plate is chosen at random, what is the probability that all three letters and all four numbers on the plate will be different? (Round your answer to three decimal places.)

Answer 1

a) The total number of ways to answer 12 questions such that no answer is repeated is computed here as the permutation of 12 answers computed as: 12!

Therefore the probability of guessing and getting every answer correct is computed here as:

= 1 / Total number of ways to answer 12 questions

= 1/12!

Therefore 1/12! = 1/479001600 is the required probability here.

b) The probability that all three letters and all four numbers on the number plate would be different is computed here as:

= Permutation of 26 letters taken 3 at a time * Permutation of 10 digits taken 4 at a time / Total ways to form the number plate of three letters and four numbers

Therefore 0.447 is the required probability here.