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.The probability is
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.The probability is
Solution
To solve this problem, we first need to understand that the question is asking for the probability of a student being either a varsity athlete or on the honor roll. This is a case of probability of A or B, which is given by P(A U B) = P(A) + P(B) - P(A ∩ B).
Here, A represents the event of being a varsity athlete, B represents the event of being on the honor roll, and A ∩ B represents the event of being both a varsity athlete and on the honor roll.
From the problem, we know that:
- There are 70 seniors who are varsity athletes, so P(A) = 70/200 = 0.35.
- There are 68 seniors who are on the honor roll, so P(B) = 68/200 = 0.34.
- There are 10 seniors who are both varsity athletes and on the honor roll, so P(A ∩ B) = 10/200 = 0.05.
Substituting these values into the formula, we get:
P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.35 + 0.34 - 0.05 = 0.64.
So, the probability that a randomly selected senior is a varsity athlete or on the honor roll is 0.64 or 64/100.
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