Question

Question: The table below gives prizes and probabilities of winning (on a single $1 ticket) for the Multi-State Powerball lottery.

Prize	Probability
$50,000	1 in 250,000
$100	1 in 2000
$10	1 in 125
$4	1 in 10

1: Find the expected value of the winnings for a single lottery ticket. Describe what this value means.

2: How much can you expect to win or lose each year if you buy 20 lottery tickets per week? Describe what this value means.

3: Should you actually expect to win or lose the exact amount from question #2? Explain your answer.

4: A player seems to consistently win $10 from this game, with 3 plays per drawing, and believes this means they’re likelihood of winning the big jackpot is higher than someone else’s. Describe what this is and why this is hazardous.

Answer 1

1.

E = sum of prize*P(prize)

= $50000*(1/250000) + $100*(1/2000) + $10*(1/125) + $4*(1/10)

= $ 0.73

Expected value = $0.73

2.

E of n games = E*n

= 0.73*(ticekts per week)*(no.of weeks)

= 0.73*(20)*(52)

= $ 759.2

3.

you cannot expect to win exacct amount the expected amount means that if you repeat this for large number of times then on average you will win this amount.

Therefore , it is not the exact amount

4.

The player is not thinking logically,

he is thinking based on only his experience and not the statistics

This mentality may lead to huge losses as he may think his probability is higher and may buy lots of tickets, therefore this may be hazardous as it may lead to huge losses

(please UPVOTE)