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 is the expected value for purchasing one ticket for the jackpot?

Explanation:

The expected value for purchasing one ticket for the jackpot is the expected value of winning less the $2 cost of the ticket which is a sure cost.

The expected value of winning is the current Powerball jackpot, which is estimated to be $193 million mutiplied by the probabilities of winning.

The probability of winning is the product of the probability of choosing the five correct white balls out of the 69 white balls and the probability of choosing the one correct red ball out of the 26 red balls.

1. Probability of choosing the five correct white balls out of the 69 white balls

How many different combinations of five different balls taken from 69 balls are there?

Note that the order does not matter; so, use the combinatory formula:

How many winning combinations are there? Just one

Thus the probability of winning is

2. Probability of choosing the correct red ball out of the 26 red balls.

That is just 1 out of 26:

3. Joint probability:

Since the two events are independent the joint probability if the product of the probabilities:

4. Expected value of winning

It is the value of the pot, $193 million multiplied by the joint probability

5. Expected value for purchasing the ticket

It is negative meaning the the expected value is a loss of $1.34

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step-by-step explanation:

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the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950