Final answer:
The probability of winning a super prize in this lottery, by either matching at least two white balls or matching the red SuperBall, is calculated to be 1/40.
Step-by-step explanation:
Calculating the Probability of Winning a Super Prize
To calculate the probability of winning a super prize in this lottery, we need to consider two separate events: matching at least two of the white balls, and matching the red SuperBall.
First, let's consider the probability of matching at least two white balls. When three balls are drawn from 10 white balls, there are combinatorial possibilities for the balls that can be drawn. The total number of ways to draw 3 balls out of 10 is given by the combination formula C(10,3) = 120. Similarly, the number of ways to choose 2 balls from your ticket's 3 balls is C(3,2) = 3, and the number of ways the remaining ball can come from the 7 balls not on your ticket is 7. Hence, the probability to match at exactly two white balls is (3 * 7) / 120.
However, since you can also win by matching all three white balls, we should add that probability as well, which is C(3,3)/C(10,3) = 1/120.
Now let's calculate the probability of matching the red SuperBall. There is just 1 correct red ball out of 10, so the probability here is 1/10.
To find the total probability of winning, we sum the probabilities of these independent events, but we have to adjust for the overlap (winning by both white and red balls, which is already counted in the white ball probability). Thus, we have:
Probability of matching at least two white balls (but not the red) = (3 * 7 + 1) / 120 = 22/120 = 11/60
Probability of matching the red SuperBall = 1/10
The total probability of winning a super prize is therefore:
(11/60) + (1/10) - (1/120)
= (22/120) + (12/120) - (1/120)
= 33/120 or 11/40, which simplifies to 1/40.
Thus, the correct answer is b) 1/40.