Question

winning the jackpot in a particular lottery requires that you select the correct five numbers between 1 and 43 and, in a separate drawing, you must also select the correct single number between 1 and 53. 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

We use the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 43$ and $r=5$. So $C(43,5)=\frac{43!}{5!(43 - 5)!}=\frac{43!}{5!×38!}=\frac{43\times42\times41\times40\times39}{5\times4\times3\times2\times1}=962598$.

Step2: Calculate number of ways to choose 1 number

There are 53 ways to choose 1 number from 53 numbers (since we are choosing 1 number out of 53), i.e., 53 ways.

Step3: Calculate total number of possible combinations

The total number of possible combinations 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 combinations is $962598\times53 = 51017694$.

Step4: Calculate probability of winning

The probability of winning is the reciprocal of the total number of combinations. So the probability $P=\frac{1}{51017694}$.

Answer:

$\frac{1}{51017694}$