In Ohio's "pick 4" lottery, you pick one of the 10,000 four digit numbers between 0000 and 9999 and (with a 1$ bet) win $5,000 if you get it correct. In terms of your expected winnings, with which game our you better off-playing " pick 4" or playing "pick 3" in which you win $500 for a correct choice of a three digit number? justify your answer please
2006-10-13 11:53:04 · 6 answers · asked by hockeyislife21 1 in Science & Mathematics ➔ Mathematics
You have a 1/10000 chance of winning $5000 and a 9999/10000 chance of winning $0. So your expected winnings are:
5000 * 1/10000 + 0 * 9999/10000. This is $0.50
For a pick 3, you have a 1/1000 chance of winning $500. So this is also an expected winning of $0.50.
The expected winnings are the same.
2006-10-13 12:01:04 · answer #1 · answered by Puzzling 7 · 0⤊ 0⤋
The average expected return on the pick 4 is 5000/10000=.5; the expected return for the pick 3 is 500/1000=.5. Therefore, you are no better off playing one game rather then the other.
2006-10-13 12:00:01 · answer #2 · answered by bruinfan 7 · 0⤊ 0⤋
The two games are mathematically equivalent. The "take" is 50% in both, so your yield is 50% as a result. Just invest $10,000 in each game and you will see that your prize money will be $5,000 from each $10,000 investment, no matter which game you choose to invest in. However, If the IRS gets involved and takes their cut of the $5,000 prize but not the (10) $500 prizes, then that swings the odds heavily in favor of pick-3.
I personally only buy lottery tickets when the bet is "even"or better. That means a 1 in 14,000,000 chance yields $14,000,000 in prize money or more. However, jackpots rarely get up to "even" status, so I rarely buy lottery tickets, which is better in the long run.
2006-10-13 12:15:53 · answer #3 · answered by Sciencenut 7 · 0⤊ 0⤋
Need to determine how many points qualify for the selection criteria over all possible points within the a circle of radius 2. Also note that the points that do not qualify for the selection criteria all lie within the unit (r = 1) circle. Area in this case captures the notion of "number of points". The area of a circle of radius 2 is 4 times larger than a unit circle. Given the points within the unit circle are less than or equal to a unit distance from the center, the probability is 1/4 of being within the unit circle. The probability of being out side the unit circle is 1 - 1/4 = 3/4 or 75%.
2016-05-21 23:51:12 · answer #4 · answered by Anonymous · 0⤊ 0⤋
For pick 4, the expected value is $5000/10000 = $0.50.
For pick 3, the expected value is $500/1000 = $0.50 again.
So, the expected winnings doesn't help you decide.
2006-10-13 11:59:47 · answer #5 · answered by James L 5 · 0⤊ 0⤋
there is the same reward to risk ratio 2:1.
if you play pick 3 you are 10 times more likely to win but you only win 1/10th the amount. if you were going.
if you were going to buy 1 of every ticket then you would play pick3 because you would lose less.
2006-10-13 13:04:49 · answer #6 · answered by ui6fu6yujt c 2 · 0⤊ 0⤋