Question

In a lottery, the top cash prize was $684 million, going to three lucky winners. Players pick five numbers from 1 to 52 and one number from 1 to 49. A player wins a minimum award of $400 by correctly matching two numbers drawn from the white balls (1 through 52) and matching the number on the gold ball (1 through 49). What is the probability of winning the minimum award?

a. 1 in 47
b. 1 in 18,564
c. 1 in 81,900
d. 1 in 107,176

Answer 1

The probability of winning the minimum award in this lottery by correctly matching two white ball numbers and the gold ball number is 1 in 107,176.

Step-by-step explanation:

The chance of winning the minimum award in this lottery involves calculating the probability of two independent events: correctly guessing two of the five numbers from the white balls drawn from a pool of 52, and separately, correctly guessing the single gold ball number drawn from a pool of 49.

First, we calculate the probability of matching two numbers from the five white balls. Since the order of the numbers doesn’t matter, we are looking at combinations, not permutations. We use the combination formula C(n, r) = n! / [r! * (n-r)!], where n is the total number of options and r is the number you need to choose. The probability of correctly picking 2 numbers out of the 5 drawn is C(5, 2) / C(52, 2).

Next, we calculate the probability of matching the gold ball number. Since there is only one gold ball number drawn from 49, this is simply a 1 in 49 chance.

Now, we multiply the probabilities of these two independent events to find the overall probability: (C(5, 2) / C(52, 2)) * (1 / 49). When you do the calculations, you’ll find the answer is 1 in 107,176 (option d).