Question

Seniors at a high school are allowed to go off campus for lunch if they have a grade of A in all their classes or perfect attendance. An assistant principal in charge of academics knows that the probability of a randomly selected senior having A's in all their classes is 0.1. An assistant principal in charge of attendance knows that the probability of a randomly selected senior having perfect attendance is 0.16. The cafeteria staff know that the probability of a randomly selected senior being allowed to go off campus for lunch is 0.18. Use the addition rule of probability to find the probability that a randomly selected senior has all As and perfect attendance.

Answer 1

Using the addition rule of probability, the probability that a randomly selected senior has both all A's and perfect attendance is 0.08, or 8%.

Step-by-step explanation:

To find the probability that a randomly selected senior has both all A's and perfect attendance, we use the addition rule of probability. The addition rule states that P(A or B) = P(A) + P(B) - P(A and B), where P(A or B) is the probability of A or B occurring, P(A) is the probability of A occurring, P(B) is the probability of B occurring, and P(A and B) is the probability of both A and B occurring. In this context, we can denote the following:

P(A) as the probability of a senior having A's in all classes, which is 0.1.

P(B) as the probability of a senior having perfect attendance, which is 0.16.

P(A or B) as the probability of a senior being allowed to go off campus for lunch, which is 0.18.

We are asked to find P(A and B), the probability that a senior has both all A's and perfect attendance. Using the addition rule, we set up the equation as follows:

P(A or B) = P(A) + P(B) - P(A and B)

0.18 = 0.1 + 0.16 - P(A and B)

Now we solve for P(A and B):

P(A and B) = P(A) + P(B) - P(A or B)

P(A and B) = 0.1 + 0.16 - 0.18

P(A and B) = 0.08

The probability that a randomly selected senior has both all A's and perfect attendance is 0.08, or 8%.

Answer 2

Given:

Probability a randomly selected senior has A = 0.1

Probability a randomly selected senior has a perfect attendance = 0.16

Probability a randomly selected senior is being allowed to go offf campus: P(A or B) = 0.18

Let's find the probability that a randomly selected senior has all As and a perfect attendance using addition rule for probability.

Apply the formula below:

P(A or B) = P(A) + P(B) - P(A and B)

Rewrite for P(A and B):

P(A and B) = P(A) + P(B) - P(A or B)

P(A and B) = 0.1 + 0.16 - 0.18

Therefore, the probability that a randomly selected senior has all As and perfect attendance is