Question

In a particular state’s lottery, you pick 5 different numbers (white balls) between 1 and 49, and a another ball (red ball) between 1 and 30 for each $1 play. Once a ball is picked, it does NOT go back in the bin and the order does NOT matter. You MUST show your work for this question (Excel is OK).

a) What is the probability of winning the big jackpot by picking all the balls, both white and red balls? What are the odds?

Answer 1

The probability of winning the big jackpot in this particular state lottery is 1 in 57,206,520, and the odds are 1:57,206,519.

Step-by-step explanation:

To calculate the probability of winning the big jackpot in this state lottery, we first need to determine the number of possible combinations for the white balls. Since the order does not matter, and a ball is not replaced once it's drawn, we use the combination formula which is C(n, r) = n! / (r! * (n-r)!) where n is the total number of balls you can choose from, and r is the number of balls you actually choose.

For the white balls, n is 49 and r is 5, so the number of combinations for the white balls is:

C(49, 5) = 49! / (5! * (49-5)!) = 1,906,884 possible combinations.

For the red ball, the number of possible outcomes is simply the number of balls you can choose from, which is 30.

The total number of combinations for both white and red balls is the product of the two:

1,906,884 (white balls) * 30 (red ball) = 57,206,520 possible combinations.

Hence, the probability of winning the big jackpot (both white and red balls) is 1/57,206,520. To express this as odds, it would be 1:57,206,519, since odds are expressed as the number of successes to the number of failures.