+0

0
96
3
+71

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?

Feb 11, 2021

#1
+1

EZ.

We compute the complement: we'll count the number of losing tickets.

We saw in part (a) that there are 1200 total possibilities.

To have a losing ticket, you must have at most one correct white ball, and miss the SuperBall.

You miss all 3 white balls if your ticket contains 3 of the 7 white numbers that were not drawn, so there are $$\binom{7}{3} = \dfrac{7 \cdot 6 \cdot 5}{6} = 35$$

You hit 1 white ball and miss the others if your ticket contains 1 of the 3 white numbers that were drawn and 2 of the 7 white numbers that were not drawn, so there are $$3\binom{7}{2} = \dfrac{3 \cdot 7 \cdot 6}{2} = 63$$.

You miss the SuperBall if you have one of the 9 red numbers that were not drawn.

Therefore, there are $$(35 + 63) \cdot 9 = 882$$ Hence, there are $$(35 + 63) \cdot 9 = 882$$ winning tickets, and your probability of winning a super prize is $$\frac{318}{1200} = \boxed{\frac{53}{200}}.$$

Feb 11, 2021
#2
0

2 ez xd

Guest Feb 11, 2021
#3
+71
0

Wow... this guest is a WIZ at math! Please makke an account :)

MathSolverForLYFE  Feb 11, 2021