Hit the Jackpot!
Roberto noticed an advertisement of the local lottery in the nearby store. One thousand lottery tickets with numbers from 000 to 999 would be sold every month, and at the end of the month, the jackpot number would be decided randomly by a modified slot machine of 3 displayed digits (each running from 0 to 9 independently) as shown in the picture.
Roberto has enough money to play the lottery 12 times. If Roberto wants to maximize his chance of winning at least once , which strategy should you suggest?
A. Buy 1 ticket each month for 12 months
B. Buy 12 different tickets in 1 month
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1 solution
If Roberto were interested in just "winning at least once", we can calculate that probability as:
Chance of "winning at least once" in 12 months = 1 - (Chance of "no winning" in 12 months)
For option A, the chance of "no winning" in each month = 1 - (Chance of "winning") = (1,000-1)/1,000 = 999/1,000.
Therefore, the chance of "no winning" in 12 months = (999/1,000)^12 ≈ 0.98806578.
For option B, the chance of "no winning" in 12 months = (1,000-12)/1,000 = 988/1,000 = 0.988
As a result, the chance of "no winning" is greater for option A, which makes the chance of "winning at least once" higher for option B.
Thus, we should suggest Roberto to use option B.