In one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (1 through 41) and matching the number on the gold ball (1 through 34). If one ticket is purchased, what is the probability of winning the jackpot?
To calculate the probability of winning the jackpot, we need to determine the total number of possible outcomes and the number of favorable outcomes.
There are 41 white balls, and we need to select 5 of them. The order does not matter, so we use combinations: 41C5 = (41!)/(5!(41-5)!) = 749398.
There are 34 possible numbers for the gold ball.
To win the jackpot, we need to match all five white balls and the gold ball. The number of favorable outcomes is 1.
Therefore, the probability of winning the jackpot is 1 favorable outcome out of 749398 possible outcomes, which simplifies to 1/749398.