Question

In a certain lottery, an urn contains balls numbered 1 to 32. From this urn, 5 balls are chosen randomly, without replacement. For a $1 bet, a player chooses one set of five numbers. To win, all five numbers must match those chosen from the urn. The order in which the balls are selected does not matter. What is the probability of winning this lottery with one ticket? The probability of winning is (Type an integer or a fraction.)

Answer 1

The probability of winning the lottery with one ticket when 5 balls are chosen from 32 without replacement is 1 / C(32, 5), resulting in a probability of 1 / (201,376).

Step-by-step explanation:

To calculate the probability of winning the lottery with one ticket when 5 balls are selected without replacement from an urn containing balls numbered 1 to 32, we use combinations since order does not matter. The total number of possible outcomes is the number of ways to choose 5 balls out of 32, which is calculated using combination formula C(n, r) = n! / (r! * (n - r)!), where n is the total number of balls and r is the number of balls chosen.

Therefore, the total number of combinations for the 5 balls drawn is C(32, 5). To calculate the probability of winning, we assume that there is only one successful outcome, as the player's set of five numbers must match exactly the set of numbers drawn from the urn.

The probability of winning the lottery with one ticket is thus 1 / C(32, 5), which simplifies to 1 / (32! / (5! * (32 - 5)!)). This results in 1 / (201,376), which is the exact probability of winning with a single lottery ticket.