In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from $1$ to $10$, and one SuperBall is draw

Question

2 months ago

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In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from $1$ to $10$, and one SuperBall is draw

n (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?

Mathematics

1 answer:

PIT_PIT [12.4K] · Answer 1 · 2026-02-18T18:52:58+03:00

Answer:

1/3

Step-by-step explanation:

We can begin with the red ball, as it presents a simpler scenario. The chances of selecting the correct number that matches the randomly drawn number is 1/10, leading to a base probability of 0.1.

Looking at the white balls, you need to accurately choose at least 2 of the drawn numbers. Assuming we select numbers 1-3, in order to win, the combinations needed are 1 and 2, 2 and 3, 1 and 3, or all three numbers 1, 2, and 3 being drawn. The probability for any pair of two being drawn is 0.075. Multiplying this by the three possible pairs gives 1/4. Additionally, the likelihood of drawing all three numbers is computed as 3/10*2/9*1/8.

Summing the probabilities gives .225 + .1 + 0.008333 = 33.333...% which simplifies to 1/3.