Question

Mega Millions is a multi-state lottery played in most U.S. states. As of this writing, the top cash prize was $656 million, going to three lucky winners in three states. Players pick five different numbers from 1 to 56 and one number from 1 to 46. Use this information to solve. Express all probabilities as fractions.

9. A player wins a minimum award of $150 by correctly matching three numbers drawn from white balls (1 through 56) and matching the number on the gold Mega Ball® (1 through 46). What is the probability of winning this consolation prize?

Answer 1

Answer:

Given that,

Here to win the lottery, player has to select the 5 numbers from the 30

i.e.,

Number of combinations = 30C5 ways

= 30!/(30-5)!*5!

= 142506

Total number of combinations = 142506

Now the probability that a player with 1 lottery ticket win is given as the ratio of number of combinations selected to that of total number of combinations

= 1 / 142506

Now if we purchase 100 tickets , then the total number of combinations selected = 100

Probability of winning if 100 different lotteries are purchased = number of combinations of 100 tickets/total number of combinations

substitute values

= 100/142506

Required probability = 50 / 71253