+311 In the SuperLottery, three balls are drawn (at random, without replacement) from white balls numbered from 1 to 12 and one SuperBall is drawn (at random) from red balls numbered from 13 to 20 When you buy a ticket, you choose three numbers from 1 to 12 and one number from 13 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?
+121 To calculate the probability of winning a super prize in the SuperLottery, we need to consider the different ways in which a ticket can win. Here are the steps to solve this problem:
1. Determine the total number of possible outcomes when drawing the balls.
2. Calculate the number of ways to win a super prize: a. Match at least two white balls: Choose 2 out of 3 winning white balls and any 1 of the remaining 9 white balls. This can be calculated as (3 2)x(9 1) . b. Match the SuperBall: Choose 1 out of 1 SuperBall from the red balls. c. Match both the SuperBall and at least two white balls: This can be calculated as the product of the number of ways to win in (a) and (b).
3. Calculate the total number of favorable outcomes for winning a super prize by summing up the results from (a), (b), and (c).
4. Determine the total number of possible outcomes by considering all ways the balls can be drawn.
5. Finally, calculate the probability of winning a super prize by dividing the total number of favorable outcomes by the total number of possible outcomes. By following these steps, you can determine the probability of winning a super prize in the SuperLottery.
