Question

In one lottery, a player wins the jackpot by matching all five numbers drawn from white balls (1 through 44) and matching the number on the gold ball (1 through 32). 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.)

Answer 1

Answer:

There is a $\frac{1}{34752256}$ probability of winning the jackpot with one ticket

Step-by-step explanation:

In order to win the jackpot, a player must select the 5 correct numbers out of the 44 possible white balls, and then the 1 out of 32 gold balls.

That means, the player has a 1-in-n-different-ways-to-choose-5-out-of-44 probability of matching the 5 white balls, and then has a 1-in-32 probability of matching the gold ball.

In order to get the probability of winning the jackpot, we multiply those two probabilities (as they are independent):

$P_{jackpot} = P_{match&white&balls} * P_{match gold ball}=\frac{1}{\left(\begin{array}{ccc}44\\5\end{array}\right) } *\frac{1}{32} =\frac{1}{34752256}$

That is a very low probability, a $2.87*10^{-6} \%$ of winning the jackpot.