Question

First, here are the payouts (Links to an external site.)Links to an external site. and probabilities for the Mega Millions lottery. Show how the probability for the grand prize jackpot is calculated to be 1 in 302, 575, 350.

Jackpot

1 in 302,575,350

$1,000,000

1 in 12,607,306

$10,000

1 in 931,001

$500

1 in 38,792

$200

1 in 14,547

$10

1 in 606

$10

1 in 693

$4

1 in 89

$2

1 in 37

Overall chances of winning any prize:

1 in 24

Answer 1

In Mega millions lottery, a player has to choose 5 numbers (without repetition) from numbers 1 through 70, and then a mega ball number from 1 to 25

There are C(70, 5) ways of choosing 5 numbers out of 70 numbers

There are 25 ways of choosing one mega ball number from 25 numbers

So, number of ways of playing the mega millions lottery = C(70, 5) * 25 = 302575350

Out of these combinations, only one combination will win

So, the probability of winning the Mega millions lottery is 1 in 302575350.