Winning the jackpot in a particular lottery requires that you select the correct five numbers between 1 and 34 ​and, in a separate​ drawing, you must also select the correct single number between 1 and 37. Find the probability of winning the jackpot.

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1 Answer

First, we work on the 5 numbers. The chance of drawing one of the correct numbers is 1/34. That leaves 33 numbers, so the probability of drawing the next number correctly is 1/33, leaving 32 numbers.

After 5 draws the probability for all 5 numbers being correct is (1/34)(1/33)(1/32)(1/31)(1/30)=1/33390720.

But the correct numbers could be drawn in any order and there are 5×4×3×2×1=120 different orders for 5 numbers, so we multiply the previous calculation by 120=1/278256.

Finally the probability of getting the correct number in the separate draw is 1/37, combined with the 5-number draw is (1/37)(1/278256)=1/10295472. That is 1 in 10,295,472 or 0.00000009713 or 0.000009713%.

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