Question

which statement best describes the use of a simulation to predict the probability that two randomly chosen people will both have their birthdays on a monday? randomly generate an integer from 1 to 2 seven times, and the probability is 1/(2)(7). randomly generate an integer from 1 to 2 seven times, and the probability is 1/2^7. randomly generate an integer from 1 to 7 two times, and the probability is 1/(2)(7). randomly generate an integer from 1 to 7 two times, and the probability is 1/7^2.

Explanation:

Step1: Analyze the number of days in a week

There are 7 days in a week. We want to find the probability that two - randomly chosen people have their birthdays on a Monday.

Step2: Determine the simulation and probability formula

To simulate the birthday of each person, we need to randomly generate an integer from 1 to 7 (where each number represents a day of the week). Since we have two people, we generate an integer from 1 to 7 two times.
The probability of one person having a birthday on a Monday is $\frac{1}{7}$. Since the events of the two people's birthdays are independent, the probability that both have their birthdays on a Monday is $\frac{1}{7}\times\frac{1}{7}=\frac{1}{7^{2}}$.

Answer:

Randomly generate an integer from 1 to 7 two times, and the probability is $\frac{1}{7^{2}}$.