Question

Miss ' X ' is fond of seeing movies. The probability that she sees a movie on the day before the test is 0.7 . Miss X is any way good at studies. The probability that she gets maximum marks in the test is 0.3 if she sees a movie on the day before the test and the corresponding probability is 0.8 if she does not see the film. If Miss ' X ' got maximum marks in the test, find the probability that she saw a movie on the day before the test.

Answer 1

Given that Miss 'X' got the maximum marks on the test, the probability that she saw a movie the day before is found using Bayes' Theorem and is approximately 46.67%.

Step-by-step explanation:

The question asks us to find the probability that Miss 'X' saw a movie the day before the test given that she received the maximum marks on her test. The situation described is a classic example of Bayes' Theorem in action, which is a way to find a conditional probability.

To solve this, let's denote seeing a movie as event M and not seeing a movie as M'. Similarly, getting maximum marks will be denoted as event A. We are given:

• P(M) = 0.7
• P(M') = 1 - P(M) = 0.3
• P(A|M) = 0.3
• P(A|M') = 0.8

We want to find P(M|A), the probability that she saw a movie given she got maximum marks. Using Bayes' Theorem:

P(M|A) = [P(A|M) * P(M)] / [P(A|M) * P(M) + P(A|M') * P(M')]

Substitute the values:

P(M|A) = [0.3 * 0.7] / [(0.3 * 0.7) + (0.8 * 0.3)]

P(M|A) = 0.21 / (0.21 + 0.24)

P(M|A) = 0.21 / 0.45

P(M|A) ≈ 0.4667

So, the probability that Miss 'X' saw a movie the day before the test given that she got maximum marks is approximately 0.4667 or 46.67%.