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. What would the minimum jackpot need to be in order to make purchasing a ticket not detrimental for the player? Round to the nearest dollar.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Using expected value, it is found that the minimum jackpot would need to be of $584,402,676.

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• A probability is the number of desired outcomes divided by the number of total outcomes.

• The expected value is given by each value multiplied by it's respective probability.

• The order in which the 5 numbers from the set of 69 is not important, which means that the combination formula is used.

• The amount is multiplied by 26, due to the red balls.

Thus, the number of total outcomes is:

$T = 26C_{69,5} = 26 \times \frac{69!}{5!64!} = 292201338$

• $\frac{1}{292201338}$ probability of winning the jackpot of x.

• $\frac{292201337}{292201338}$ probability of losing $2.

The minimum expected value that makes the game fair is 0, thus:

$\frac{1}{292201338}x - \frac{292201337}{292201338}(2) = 0$

$x - 2(292201337) = 0$

$x = 584402676$

The minimum jackpot would need to be of $584,402,676.

A similar problem is given at https://brainly.com/question/24919082