Question

The current Powerball jackpot is estimated to be $193 million. The Powerball lottery is decided every Wednesday and Saturday night by drawing five white balls out of a drum with 69 balls and one red ball out of a drum with 26 red balls. The Powerball jackpot is won by matching all five white balls in any order and the red Powerball. Each ticket costs $2. A ticket is defined as a set of five white and 1 red number.

Answer 1

"2.660503478" would be the right answers to the key statement.

Explanation:

Drawing 5 balls out of 69 can be done in (
`(69)/(5)`)

=
`(69* 68* 67* 66* 65)/(5!)`

Drawing 1 ball out of 26 red balls can be done in (
`(26)/(1)`)

=
`26`

Then the chance of drawing 5 out of 69 balls including 1 out of 26 red balls and then both matching the jackpot

=
`(1)/(11238513* 26)`

=
`(1)/(292201338)`

Since the sum of the jackpot is $193-106 and then one ticket costs $2, the estimated value of buying one ticket again for jackpot is $2.

=
`(1)/(292201338)* 193* 10^6+(292201338-1)/(292201338)* 2`

=
`2.660503478`