Question

In a school, there are two science sections in class X11. Section A has 80 students, out of which 50% are girls. Section B has 100 students, out of which 80% are girls. If a student is randomly selected and found to be a boy, what is the probability that he is from Section A?

A) Probability of selecting a boy from Section A is 50%
B) Probability of selecting a boy from Section B is 20%
C) Probability of selecting a boy from Section A is 10%
D) Probability of selecting a boy from Section B is 80%

Answer 1

The probability of selecting a boy from Section A is 66.67%, calculated by dividing the number of boys in Section A (40) by the total number of boys in both sections (60). The provided options do not contain the correct probability.

Step-by-step explanation:

To find the probability that a randomly selected boy is from Section A, we need to use Bayes' theorem or a straightforward approach with conditional probability. To solve this problem, we'll first identify the total number of boys in both sections:

• Section A has 80 students, with 50% being girls, so there are 40 boys (100% - 50% of 80).
• Section B has 100 students, with 80% being girls, so there are 20 boys (100% - 80% of 100).

The total number of boys in both sections is 60 (40 from A and 20 from B).

The probability that a boy is from Section A is the number of boys in Section A divided by the total number of boys:

Probability = Number of boys in Section A / Total number of boys = 40 / 60 = 2/3 or approximately 66.67%.

This means the correct answer is: Probability of selecting a boy from Section A is 66.67%, which is not one of the provided options, so there might be a mistake in the options given. Each of the choices provided in the original question does not accurately represent the correct probability.