Question

Powerball is a multistate lottery in which 5 white balls from a drum with 53 balls and 1 red ball from a drum with 42 red balls are selected. For a \(1 ticket, players get one chance at winning the jackpot by matching all 6 numbers. What is the probability of selecting the winning numbers on a \)1 play?

Short answer

The probability of winning numbers is approximately$0.0022$

Step-by-step solution

Step 1. Given information

There are 53 white balls in the drum and 5 white balls are selected.

There are 42 red balls in a drum and 1 red ball is selected.

The player wins the jackpot if all 6 numbers matches.

Step 2. To find probability of selecting 5 white balls from the drum.

The number of favorable outcomes is 5.

The number of possible outcomes is 53.

The probability of selecting 5 white balls out of 53 balls is:

$P\left(w\right)=\frac{5}{53}$

Step 3. To find probability of selecting 1 red balls from the drum.

The number of favorable outcomes is 1.

The number of possible outcomes is 42.

The probability of selecting 1 white balls out of 42 balls is:

$P\left(r\right)=\frac{1}{42}$

Step 4. To find probability of selecting winning numbers.

Since the player will win when 5 white balls and 1 red ball are selected.

Hence, the probability of winning numbers is:

$$\begin{gathered} P=P\left(w\right)\times P\left(r\right) \\ =\frac{5}{53}\times \frac{1}{42} \\ =\frac{5}{2226} \\ \approx 0.0022 \end{gathered}$$