Question

3. In New York, the Mega Ball jackpot lottery asks you to pick 5 numbers (integers) from 1 to 59 (the "upper

section") and then pick a Mega Ball number from 1 to 35 (the "lower section"). You win $10,000 if you
match exactly 4 of the 5 numbers from the upper section and match the Mega Ball number from the
lower section. The winning number or numbers for each section are chosen at random without
replacement. Determine the probability of correctly choosing exactly 4 of the winning numbers and the
Mega Ball number.

Answer 1

P = 0.000000028514

Explanation:

First we are going to calculate the probability of correctly choosing exactly 4 of the winning numbers.

Remember that the probability of an event can be calculated thus:

`P = (favourable - cases)/(total -cases)`

The favorable cases resulting from choosing 4 numbers of the set of 5 winning numbers from the upper section.

The favorable cases can be calculated with a combinatorial thus:

`5C4 = (5!)/((5-4)!4!) =5`

and the total cases are:

`59C5 = (59!)/((59-5)!5!) = 5006386`

Then the probability is:

`P = (5)/(5006386) = 0.000000998`

and the probability of correctly choosing the Mega Ball number is:

`P = (1)/(35)` = 0.0285714

And how both events are independent the probability of correctly choosing exactly 4 of the winning numbers and the Mega Ball number is:

P = (0.000000998)(0.0285714)

P = 0.000000028514