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?

Question

Mathematics

Amanda Holt

6 November, 13:05

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?

+2

Answers (1)

Know the Answer?

Tatiana Booth · Answer 1

0.00008710

Step-by-step 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