Problem 7CRE

Vermont Hot Lotto Winning the jackpot in the Vermont Hot Lotto game requires that you select five numbers between 1 and 39 and another number between 1 and 19. The first five numbers must match (in any order) the same five numbers that are later drawn, and the sixth number must also match the sixth number that is later drawn.

a. What is the probability that the first five selected numbers match the five numbers that are later drawn?

b. What is the probability that the sixth selected number matches the sixth number that is later drawn?

c. What is the probability of winning the jackpot?

Solution 7CRE

(a)

To choose 5 different numbers from 1 to 39 (order does not matter) combination rule must be used. So the possible number of ways to choose 5 numbers out of 39 numbers is

= 575,757

Out of these 575,757 possible ways only one way is corresponding to the five numbers that are later drawn so the probability that the first five selected numbers match the five numbers that are later drawn is

P(match the first five numbers later drawn = 1/575,757

Hence, the probability that the first five selected numbers match the five numbers that are later drawn is 1/575,757.

(b)

Sixth number is drawn from the numbers between 1 and 19 so the probability that the sixth selected number matches the sixth number that is later drawn is

P(match the sixth number later drawn) = 1/19

Hence, the probability that the sixth selected number matches the sixth number that is later drawn is 1/19.

For winning the jackpot all the six numbers must be match so the probability of winning is

P (winning) = P (match the first five numbers later drawn)

.P (match the sixth number later drawn)

= 1/19 . 1/575,757

= 1/10,939,383

Hence, the probability of winning is.1/10,939,383