Questions: Suppose the probability of winning a particular lottery is 1 in 15C5+8 or 1/24,024. If Juanita and Michelle each play the lottery on one particular evening, what is the probability that both will select the winning numbers if they make their selections independently of each other? The probability that both will select the winning numbers is approximately

Suppose the probability of winning a particular lottery is 1 in 15C5+8 or 1/24,024. If Juanita and Michelle each play the lottery on one particular evening, what is the probability that both will select the winning numbers if they make their selections independently of each other? The probability that both will select the winning numbers is approximately
Transcript text: Suppose the probability of winning a particular lottery is 1 in ${ }_{15} \mathrm{C}_{5}+8$ or $\frac{1}{24,024}$, If Juanita and Michelle each play the lottery on one particular evening, what is the probability that both will select the winning numbers it they make their selections independently of each other? The probability that both will select the winning numbers is approximately $\square$ (Use scientfic notation. Use the multiplication symbol in the math palette as needed. Round to the nearest hundredth as needed.)
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Solution

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Solution Steps

Step 1: Calculate the total number of possible winning combinations

Given $n = 15$, $k = 5$, and $m = 8$, we calculate $N = { }_{n}C_{k} \cdot m = \frac{n!}{k!(n-k)!} \cdot m$. Thus, $N = \frac{15!}{5!(15-5)!} \cdot 8 = 24024$.

Step 2: Calculate the probability of one individual winning the lottery

The probability of winning for one individual is $\frac{1}{N} = \frac{1}{24024}$.

Step 3: Calculate the probability that both individuals win

Since the selections are independent, the probability that both A and B win is $\left(\frac{1}{N}\right)^2 = 0$.

Final Answer: The probability that both individuals win the lottery, rounded to 2 decimal places, is 0.

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