Question

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

Answer 1

Answer:

P = 0.000000028514

Step-by-step 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:

$P = \frac{favourable - cases}{total -cases}$

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:

$5C4 = \frac{5!}{(5-4)!4!} =5$

and the total cases are:

$59C5 = \frac{59!}{(59-5)!5!} = 5006386$

Then the probability is:

$P = \frac{5}{5006386} = 0.000000998$

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

$P = \frac{1}{35}$ = 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