Chapter 13.3, Problem 73AYU

To determine

To find: What is the probability of selecting the winning numbers on a $\$2$ play?

Answer to Problem 73AYU

$0.000033069$

Explanation of Solution

Given:

Powerball is a multistate lottery in which 5 white balls from a drum with 69 balls and 1 red ball from a drum with 26 balls are selected. For a $\$2$ ticket, players get one chance at winning the jackpot by matching all 6 numbers.

Formula Used:

If $S$ is the sample space of this experiment,

$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$

Calculation:

The selection of first ball can be any 10.

The selection of second ball can be any one from remaining 9.

The selection of third ball can be any one from remaining 8.

The selection of fourth ball can be any one from remaining 7.

The selection of fifth ball can be any one from remaining 6.

Hence the sample space has $10\ast 9\ast 8\ast 7\ast 6=30240$ elements.

Probability of selecting one ball (a winning one) $=\frac{1}{30240}\approx 0.000033069$.