Question

Out of 200 students in a senior class, 10 students are varsity athletes and on the honor roll. There are 70 seniors who are varsity athletes and 68 seniors who are on the honor roll. What is the probability that a randomly selected senior is a varsity athlete or on the honor roll? Write your answer as a fraction in simplest form or as a decimal.

Answer 1

Answer: We can use the formula:

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

where A and B are two events.

In this case, we want to find the probability that a randomly selected senior is a varsity athlete or on the honor roll. We can define the events as follows:

A = the event that a senior is a varsity athlete

B = the event that a senior is on the honor roll

From the problem statement, we know:

P(A and B) = 10/200 = 1/20

P(A) = 70/200 = 7/20

P(B) = 68/200 = 17/50

Plugging these values into the formula:

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

= 7/20 + 17/50 - 1/20

= 21/50

Therefore, the probability that a randomly selected senior is a varsity athlete or on the honor roll is 21/50.

Answer 2

The probability that a randomly selected senior is either a varsity athlete or on the honor roll is 16/25, which can also be expressed as the decimal 0.64.

Step-by-step explanation:

The question you're asking relates to finding the probability that a randomly selected senior is either a varsity athlete or on the honor roll. This is a classic example of a probability question involving the union of two sets.

First, we need to consider the total number of students which is 200. There are 70 varsity athletes and 68 students on the honor roll. However, since 10 students are counted in both groups (varsity athletes and honor roll), we need to adjust our count so that we don't double-count these students when we combine the two groups. We use the formula:

Probability (A or B) = (Number of A) + (Number of B) - (Number of both A and B) / (Total number of students)

Using the figures from your question, we calculate the probability as follows:

Probability (Varsity Athlete or Honor Roll) = (70 varsity athletes + 68 honor roll students - 10 who are both) / 200 students = 128/200

The fraction 128/200 can be reduced to the simplest form by dividing both the numerator and the denominator by the greatest common divisor, which is 8. This simplifies the fraction to 16/25.

To convert it to a decimal, you divide 16 by 25, which is 0.64.

So, the probability that a randomly selected senior is either a varsity athlete or on the honor roll is 16/25 or 0.64.