In a classic Simpsons episode, Homer has 50 lottery tickets. When the first number is called, it is revealed that none of his 50 tickets has that number. Marge reminds him he can win something if he gets 5 of 6, but again, on the second number, none of his 50 cards has that number. Assuming the numbers used are the same as in Powerball, what is the formula for figuring out the odds of not getting any of 2 numbers on any of 50 tickets?

If the probability of not getting the first two numbers is p, then the probability of missing all 50 lottery tickets is p[sup]50[/sup]. Assuming it’s your standard “pick a number from 1 to 49” lottery, p = 47/49 (that’s 48/49 * 47/48), and the probability of not getting any right is a little over .12.

Thanks! What is that in actual odds against this happening?

3 to 22 against.

Though IIRC, the disclaimer at the end of the lottery ad said actualoddsofwinningoneinsixhundredmillion , so maybe the number range isn’t the same as the real Powerball?

Also, notice how Homer seems to know *immediately* that neither number is on any of his tickets? Either he has an amazing memory, or (more likely) he picked the same numbers for all 50 tickets, thinking that this will somehow increase his odds of winning. Pretty stupid, but Homer isn’t exactly known for his sharp intellect.