Question

winning the jackpot in a particular lottery requires that you select the correct five numbers between 1 and 29 and, in a separate drawing, you must also select the correct single number between 1 and 44. find the probability of winning the jackpot. the probability of winning the jackpot is . (type an integer or simplified fraction.)

Explanation:

Step1: Calculate number of ways to choose 5 numbers from 29

The number of combinations of choosing $r$ items from $n$ items is given by the formula $C(n,r)=\frac{n!}{r!(n - r)!}$. Here, $n = 29$ and $r=5$. So, $C(29,5)=\frac{29!}{5!(29 - 5)!}=\frac{29!}{5!×24!}=\frac{29\times28\times27\times26\times25}{5\times4\times3\times2\times1}=118755$.

Step2: Calculate number of ways to choose 1 number from 44

There are 44 ways to choose 1 number from 44, since $C(44,1)=\frac{44!}{1!(44 - 1)!}=\frac{44!}{1!×43!}=44$.

Step3: Calculate total number of possible outcomes

The total number of possible outcomes for the lottery is the product of the number of ways to choose 5 - number combination and 1 - number combination. So the total number of outcomes is $118755\times44 = 5225220$.

Step4: Calculate probability of winning

The probability $P$ of winning the jackpot is the ratio of the number of favorable outcomes (which is 1) to the total number of possible outcomes. So $P=\frac{1}{5225220}$.

Answer:

$\frac{1}{5225220}$