In the powerball lottery, you first pick five numbers from a field of 59, then o

Question

In the powerball lottery, you first pick five numbers from a field of 59, then one number (the powerball) from a field of 39. To win the jackpot, say $50 million, you must match all 6 numbers. To win some prize, you must hit the powerball or matach at least 3 of 5 from the field of 59.

a) What are your chances of winning the jackpot in the powerball lottery? If it's better than 1 in 50 million, does it "pay off" to pay the lottery?

b) The chance of winning any prize is reported as approximately 1 in 35. What are the exact chances?

Explanation / Answer

I'm not sure how to do part b (sorry!)... but here is part A explained

(a) to win the jackpot you have to match a number out of 59 five times, and also 1 number out of 39

(1/59)*(1/59)*(1/59)*(1/59)*(1/59)*(1/39) = 1/(2.7882*1010) 1 in 2.7882*1010 chance

your chances are much smaller than 50 million, it doesn't pay off; you'd have to play way over 50 million times before you win anything (in the end you'd still lose money even if you won)

hope this helps a bit

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