In a certain high school class, consisting of 60 girls and 40 boys , it is observed that 24 girls and 16 boys wear eyeglasses. If a student is picked at rondom from this class, the probability that the student wears eyeglasses is 40/100. what is the probability that a student picked at rondom given that is a boy wears eyeglasses?

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To calculate the probability that a student picked at random, given that the student is a boy, wears eyeglasses, we need to use conditional probability.

Let's denote the event "a student wears eyeglasses" as A, and the event "a student is a boy" as B.

We know that the probability of A is 40/100, which means P(A) = 40/100 = 0.4.

We also know that the probability of being a boy is P(B) = 40/100 = 0.4, since there are 40 boys out of 100 students.

To calculate the probability that a student is a boy given that the student wears eyeglasses (P(B|A)), we can use the formula for conditional probability:

P(B|A) = P(A and B) / P(A)

P(A and B) represents the probability that a student is both a boy and wears eyeglasses. We know that 16 boys wear eyeglasses, so P(A and B) = 16/100 = 0.16.

Now we can calculate P(B|A):

P(B|A) = (P(A and B)) / P(A)
= (0.16) / (0.4)
= 0.4

Therefore, the probability that a student picked at random given that they are a boy, wears eyeglasses is 0.4 or 40%.

To find the probability that a student picked at random, given that the student is a boy, wears eyeglasses, you need to use conditional probability.

Conditional probability is the probability of an event occurring given that another event has already occurred. In this case, we want to find the probability that the student wears eyeglasses given that the student is a boy.

Let's denote:
- A: Event that a student wears eyeglasses
- B: Event that a student is a boy

The probability of A given B, denoted P(A|B), can be calculated using the formula:

P(A|B) = P(A and B) / P(B)

We know that the probability of a student wearing eyeglasses is 40/100, which can be written as P(A) = 40/100.

To calculate P(A and B), we need to find the probability that a student is both a boy and wears eyeglasses. We know that 16 boys wear eyeglasses, so P(A and B) = 16/100.

The probability of a student being a boy is 40/100, which can be written as P(B) = 40/100.

Now, we can calculate the probability that a student picked at random, given that the student is a boy, wears eyeglasses:

P(A|B) = P(A and B) / P(B) = (16/100) / (40/100) = 16/40 = 0.4

Therefore, the probability that a student picked at random, given that the student is a boy, wears eyeglasses is 0.4 or 40%.

How many boys there are in the group that wears glasses over the total number of people that wear glasses.

Remember to simplify.