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# Tough Question

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So I saw someone post this question, and I saw the solution that I didn't understand: https://web2.0calc.com/questions/extremely-tricky. It said that the probability should be closer to 1/4. But why? Also, I don't know how to solve this problem.

In the SmallState Lottery, three white balls are drawn (at random) from ten balls numbered 1 through 10, and a blue SuperBall is drawn (at random) from ten balls numbered 11 through 20. When you buy a ticket, you select three numbers from 1-10 and one number from 11-20. To win the jackpot, the numbers on your ticket must match the three white balls and the SuperBall. (You don't need to match the white balls in order).

If you buy a ticket, what is your probability of winning the jackpot?

Feb 5, 2020

#1
+18875
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To find the probability of the three white balls:

You have to select all of the winning balls; in other words, you have to select three winning balls from three winning balls, and this can be done in 3C3 ways (which is just 1 way).

You also have to select none of the losing balls, in other words, you have to select zero losing balls from seven losing balls, and this can be done in 7C0 ways (which, also, is just 1 way).

Then, you have to divide this result from the total number of ways that 3 balls can be drawn from 10 balls, and this can be done in 10C3 ways (which is 120 ways).

Summarizing:     [ 3C3 · 7C0 ] / 10C3   =  1 · 1 / 120  =  1/120.

You also have to select the SuperBall. Since there are 10 possibilities and you must select the 1 that is the winner, your probability of selecting the SuperBall is  1/10.

Your probability of selecting all three white balls and the SuperBall is:  (1/120) · (1/10)  =  1/1200.

Feb 6, 2020
#2
+302
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Thank you so so much!

AnimalMaster  Feb 6, 2020
#3
+108675
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The other question was different.

I answered the other one recently but obviously not on the thread that you just found.

Feb 12, 2020