Question

The Sad State Lottery requires you to select a sequence of four different numbers from 0 through 42. (Order is important.) You are a Giant Winner if your sequence agrees with that in the drawing, and you are a Prize Winner if your selection of numbers is correct, but in the wrong order. (Enter your answers as fractions.) What is the probability of being a Giant Winner?

Answer 1

0.00008710

Explanation:

Probability of becoming Winner (A)= 1 / (42 P 3)

[42 P 3 because the order is important]

= 1 / [42! / (39!)] = 0.00000145

Probability of being a Prize Winner (B)= 1 / 42 C 3

[42 C 3 because the order is not important]

= 1 / [42! / (39!)(3!)] = 0.00008710

Probability that you are either a Winner or a Prize Winner = P(A U B) = P(A) + P(B) - P(A and B)

P(A and B) = P(A) as being a winner and prize winner is the same as being the winner.

So, Probability that you are either a Winner or a Prize Winner = P(A) + P(B) - P(A)

P(B) = 0.00008710