Question

this question: 1 point(s) possible
in one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (1 through 45) and matching the number on the gold ball (1 through 31). if one ticket is purchased, what is the probability of winning the jackpot?

the probability of winning the jackpot with one ticket is
(type an integer or a simplified fraction.)

Explanation:

Step1: Calculate white ball combinations

We need the number of ways to choose 5 distinct white balls from 43, which uses combinations:
$$\binom{43}{5} = \frac{43!}{5!(43-5)!} = \frac{43\times42\times41\times40\times39}{5\times4\times3\times2\times1} = 962598$$

Step2: Calculate gold ball outcomes

There are 31 possible gold ball numbers, so 31 total outcomes for the gold ball.

Step3: Find total possible tickets

Multiply white ball combinations by gold ball outcomes to get total possible ticket combinations:
$$962598 \times 31 = 29840538$$

Step4: Compute winning probability

There is only 1 winning combination, so probability is $\frac{1}{\text{total combinations}}$.

Answer:

$\frac{1}{29840538}$