Interview Question: Impossible Odds

Sample Question #309 (probability theory)
Another fun brainteaser-type question involving odds.
The odds of winning the Powerball lottery in the U.S. on one ticket is 1 in 195,249,054. ($1 buys one ticket.) How many $1 tickets do you have to play in order to have a probability of more than 1/2 to win the jackpot (grand prize) at least once in the games you have played? Does it make a difference if you buy one ticket per drawing, 10 tickets per drawing, or 1000 tickets per drawing? Also, does it make a difference if you play different numbers each time, or stick with the same numbers all the time?
[Disclaimer: this is absolutely not a promotion of any kind of lottery! This is just a sample interview question that tests your probability theory knowledge]
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2 Responses to Interview Question: Impossible Odds

  1. Brett says:

    ANSWERThe odds of not winning on one ticket is simply 1-Pr(win on one ticket) = 0.999999994878336. Then, just find the x that solves 0.999999994878336^x <= 0.5. Using logs, you find x = 135,336,330.It doesn’t matter how you play, as long as you play different numbers on different tickets (otherwise all your tickets would count as one ticket and you would have wasted your money!).

  2. Brett says:

    Oh, here’s another fun fact: if you play $1000 per game, and there’re two games per week, it would take you 1,300 years to reach the even odds. Of course, lottery is just a form of legalized gambling, which means most players will lose.

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