+355 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 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?
+607 To calculate the probability of winning the jackpot, we need to find the probability of two independent events happening:
1. Matching the three white balls.
2. Matching the red SuperBall.
Let's calculate each probability separately:
1. **Matching the three white balls:**
Since the white balls are drawn without replacement, the probability of matching the first number on your ticket is 1 out of 12, the second number is 1 out of 11, and the third number is 1 out of 10. This is because each time a ball is drawn, there is one fewer ball left in the pool.
So, the probability of matching the three white balls is:
\[\frac{1}{12} \times \frac{1}{11} \times \frac{1}{10}\]
2. **Matching the red SuperBall:**
There is only one red SuperBall drawn, and you have one chance out of 8 (from 13 to 20) to match it.
So, the probability of matching the red SuperBall is:
\[\frac{1}{8}\]
Now, to find the probability of winning the jackpot, we multiply the probabilities of both events happening:
\[P(\text{Winning jackpot}) = P(\text{Matching three white balls}) \times P(\text{Matching red SuperBall})\]
\[= \left(\frac{1}{12} \times \frac{1}{11} \times \frac{1}{10}\right) \times \frac{1}{8}\]
\[= \frac{1}{12 \times 11 \times 10 \times 8}\]
\[= \frac{1}{10560}\]
So, the probability of winning the jackpot is \( \frac{1}{10560} \).
