Question

In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from $1$ to $10$, and one SuperBall is drawn (at random) from ten red balls numbered from $11$ to $20$. When you buy a ticket, you choose three numbers from $1$ to $10,$ and one number from $11$ to $20$.
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?

Answer 1

Answer:

1/3

Step-by-step explanation:

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 atleast 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. You can calculate the probability for each of these cases. 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