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Rules: Pick 5 numbers out of 75 and 1 MegaBall number out of 15. See if your num

ID: 3204185 • Letter: R

Question

Rules: Pick 5 numbers out of 75 and 1 MegaBall number out of 15. See if your numbers match the numbers selected at the next drawing. What is your chance of winning the Jackpot in one try? What is your chance of not winning the Jackpot in one try? What is your chance of not winning the Jackpot at all if you try once a day for N days? [Note that, for small x, (1-x)^n = (1 - nx).] What is your chance of winning the Jackpot at least once if you try once a day for N days? How many times would you need to play to have a 1/3 chance of winning the Jackpot at least once? [Note that, for small x, log(1-x) = (-x).]

Explanation / Answer

A) Probability of getting 5 numbers and megaball right in 1 try = 5x4x3x2x1x(1/75)5x(1/15) = 3.371x10-9

b) Probability of no winning jackpot on 1 try = 1 - 3.37x10-9

= 0.9999999966

C) P(no winning jackpot on N tries) = (1-3.37x10-9)n

= 1 - nx3.37x10-9

D) P(winning jackpot at least once on N tries =Nx3.37x10-9

E) Nx3.37x10-9 = 1/3

So, N = 98876953