Question

In a class of 40 students 25 have opted Hindi as second language (event A). 35 students got first class (event B) in the examinations of which 20 had taken Hindi as second language. It is found that a student picked at random has secured first class. The probability P(A/B) that this student has taken Hindi as second language is______

(a)4/7
(b)5/8
(c)7/8
(d)1/2​

Answer 1

The correct answer to the probability that a student picked at random has taken Hindi as a second language, given that they have secured first class, is 4/7.

Step-by-step explanation:

Let's use conditional probability to find the probability P(A/B) that a student who got first class has taken Hindi as a second language. We know that P(B) = 35/40, which represents the probability of getting first class regardless of the language chosen. And we are given that P(A AND B) = 20/40, which represents the probability of getting first class and having Hindi as a second language.

To find P(A/B), we can use the formula: P(A/B) = P(A AND B) / P(B). Plugging in the values, we get: P(A/B) = (20/40) / (35/40) = 20/35 = 4/7.

The question revolves around the concept of conditional probability, specifically the probability of a student having opted for Hindi as a second language given that they have secured first class in a class of 40 students. We are given that 25 out of 40 students have taken Hindi (event A) and 35 students got a first-class grade (event B). Of the first-class students, 20 have taken Hindi. We are required to find the probability P(A/B).

We apply the formula for conditional probability: P(A/B) = P(A ∩ B) / P(B).

Here, P(A ∩ B) is the probability that a student has taken Hindi as a second language and got a first class, which is 20 out of 40, or 1/2. P(B) is the probability of getting a first class, which is 35 out of 40, or 7/8.

So, P(A/B) = (1/2) / (7/8) = (1/2) * (8/7) = 4/7.

Therefore, the correct answer is (a) 4/7.