Question

A lottery game has players selecting 4 numbers at random from the numbers 1–60. The state picks 20 winning numbers. If the​ player's 4 numbers are selected by the​ state, the player wins. What is the probability of​ winning?

How many ways can the 4 numbers be chosen from the original 60 ​numbers, regardless of whether they are in the winning group or the losing​ group?

Answer 1

To find the probability of winning the lottery game, use the combination formula to determine the number of ways the player can select their 4 numbers from the original 60 numbers. Then, divide the number of winning outcomes by the total number of possible outcomes.

To find the probability of winning the lottery game, we need to determine the number of ways the player can select their 4 numbers from the original 60 numbers. This can be done using the combination formula:

C(n, k) = n! / (k!(n-k)!)

Where n is the total number of numbers (60) and k is the number of numbers the player is selecting (4).

C(60, 4) = 60! / (4!(60-4)!)

C(60, 4) = 60! / (4!56!)

C(60, 4) = (60 × 59 × 58 × 57) / (4 × 3 × 2 × 1)

C(60, 4) = 913,950

The number of ways the player can select their 4 numbers is 913,950. The probability of winning is the number of winning outcomes (1) divided by the total number of possible outcomes (913,950).

P(win) = 1 / 913,950

Therefore, the probability of winning the lottery game is approximately 0.000001094 or 0.0001094%.