Question

In a class of 40 students, 18 are male and 22 are female. two thirds of the male students and one half of the female students passed the final exam. what is the probability that one student chosen at random passed the exam or is a male?

Answer 1

1

Explanation:

To find the probability that a randomly chosen student passed the exam or is a male, we'll calculate the probability of each event separately and then add them together.

1. Probability that a randomly chosen student is male:

There are 18 males out of a total of 40 students, so the probability is 18/40.

2. Probability that a randomly chosen student passed the exam:

For males, two-thirds (2/3) passed the exam, which is (2/3) * 18 = 12 males.

For females, half (1/2) passed the exam, which is (1/2) * 22 = 11 females.

So, the total number of students who passed the exam is 12 (males) + 11 (females) = 23 out of 40.

Now, let's calculate the probability for each event:

1. Probability of being male = 18/40 = 9/20

2. Probability of passing the exam = 23/40

To find the probability of either event occurring (passed the exam or is a male), we can add these probabilities:

Probability (passed the exam or is a male) = Probability of being male + Probability of passing the exam

Probability (passed the exam or is a male) = (9/20) + (23/40)

To add these fractions, we need a common denominator, which is 40:

Probability (passed the exam or is a male) = (18/40) + (23/40)

Now, add the numerators:

Probability (passed the exam or is a male) = (18 + 23)/40

Probability (passed the exam or is a male) = 41/40

Since probabilities are usually expressed as values between 0 and 1, this probability should be reduced to a value between 0 and 1. In this case, it would be 1 because it's impossible to have a probability greater than 1.

So, the probability that a randomly chosen student passed the exam or is a male is 1.