Question

in one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (1 through 43) and matching the number on the gold ball (1 through 33). 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 the number of ways to choose 5 white balls

The formula for combinations is \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 43\) (number of white balls) and \(r=5\) (number of white balls drawn).

$$
LATEXBLOCK0
$$

Step2: Calculate the number of ways to choose 1 gold ball

There are \(n = 33\) gold balls and \(r = 1\) gold ball is drawn. Using the combination formula \(C(n,r)=\frac{n!}{r!(n - r)!}\), with \(n=33\) and \(r = 1\)

$$
LATEXBLOCK1
$$

Step3: Calculate the total number of possible outcomes

By the multiplication principle, the total number of possible outcomes for the lottery is the product of the number of ways to choose white balls and the number of ways to choose gold balls. So the total number of outcomes \(N=C(43,5)\times C(33,1)\)

$$N=962598\times33 = 31765734$$

Step4: Calculate the probability

The probability \(P\) of winning (since there is only 1 winning combination) is given by \(P=\frac{1}{N}\)

$$P=\frac{1}{31765734}$$

Answer:

\(\frac{1}{31765734}\)