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1) In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from  to , and one SuperBall is drawn (at random) from ten red balls numbered from  to . When you buy a ticket, you choose three numbers from  to  and one number from  to .

If the numbers on your ticket match the three white balls and the red SuperBall, then you win the jackpot. (You don't need to match the white balls in order). What is the probability that you win the jackpot?

 

2) In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from  to , and one SuperBall is drawn (at random) from ten red balls numbered from  to . When you buy a ticket, you choose three numbers from  to  and one number from  to .

If the numbers on your ticket match at least two of the white balls or match the red SuperBall, then you win a super prize. What is the probability that you win a super prize?

 

I tried this problem multiple times, but all of my attempts were incorrect. Can someone please help?

 Jan 20, 2021
 #1
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1)  since you have to choose three numbers and one superball to win the lottery, your chances will be:

chances of getting the 3 white numbers = 1/6*1/10 x 1/9 x 1/8 = 1/4320

chance of getting the superball = 1/10

chances of winning the jackpot = 1/4320 x 1/10 = 143200

 

2)

On average, 1 out of 10 times you will draw the AwesomeBall (and this wins all by itself so we don't care what the other balls are) for a winning probability of 0.10.

 

Now, for the 9 out of ten times that you do not draw the AwesomeBall:

We will have to get a losing blue ball, I'll call that B (and the probability of getting that losing ball is 0.90).

We can win by getting two or more of the white balls. I'll classify a winning white ball (whose probability is 1/10 = 010)

as W and a losing white ball as L (whose probability is 9/10 = 0.90).

So, we can still win if we have this:

B x W x W x W   =   (0.90) x (0.10) x (0.10) x (0.10)   =  0.0009

B x W x W x L    =   (0.90) x (0.10) x (0.90) x (0.10)   =  0.0081

B x W x L x W    =   ...

B x L x W x W    =   ...

 

Since these are independent, add the above 5 results together:  317/2500

 Jan 20, 2021
 #4
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Both are wrong :(

Guest Jan 20, 2021
 #2
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2)     Lets start with the red ball because it is easier. You have 1/10 chances to pick the same number that is drawn randomly. Thus your base probability is .1 Now going to the white balls, you need 2 numbers picked as the numbers drawn. Let's say we pick numbers 1-3. In order to win, the numbers 1 and 2, 2 and 3, 1 and 3, or 1 2 and 3 must be drawn. In the case only 2 are drawn, the probability for each is 0.075. Since there are three cases that this could happen, you multiply this probability by 3, becoming 1/4. However, there is also the chance that you get all three. The probability of this is 3/10*2/9*1/8.

.225 + .1 + 0.008333  = 33.333...% or 1/3

 

Don't want to tackle numero 1 for now...

 Jan 20, 2021
 #3
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Sorry, I already trired that answer already, and it's wrong :/

Guest Jan 20, 2021
 #5
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Hello, dear

I am not sure that what is the perfect answer to this question. But according to my opinion below answer is best for it

Lets start with the red ball because it is easier. You have 1/10 chances to pick the same number that is drawn randomly. Thus your base probability is .1 Now going to the white balls, you need 2 numbers picked as the numbers are drawn. Let's say we pick numbers 1-3. In order to win, the numbers 1 and 2, 2 and 3, 1 and 3, or 1 2 and 3 must be drawn. In the ome tv case only 2 are drawn, the probability for each is 0.075. Since there are three cases that this could happen, you multiply this probability by 3, becoming 1/4. However, there is also the Chatiw chance that you get all three. The probability of this is 3/10*2/9*1/8.

.225 + .1 + 0.008333  = 33.333...% or 1/3

 

Don't want to tackle numero 1 for now...

Love from canada.

 Jan 21, 2021
 #6
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+6

Vivek, I believe we have the same answer, but anyways, Guest could you specify where you think I got the problem wrong?

 Jan 27, 2021

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