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For a group of students, 30%, 40% and 50% failed in Physics, Chemistry and at least one of the two subjects
respectively. If an examinee is selected at random, what is the probability that he passed in physics if it is known that
he failed in Chemistry?
(a) 1/2 (b) 1/3 (c) 1/4 (d) 1/6?
Most Upvoted Answer
For a group of students, 30%, 40% and 50% failed in Physics, Chemistry...
Given Information:
- 30% failed in Physics
- 40% failed in Chemistry
- 50% failed in at least one of the two subjects

Calculation:
Let's assume the total number of students is 100 for easier calculations.
- Number of students who failed in Physics = 30% of 100 = 30 students
- Number of students who failed in Chemistry = 40% of 100 = 40 students
- Number of students who failed in at least one subject = 50% of 100 = 50 students

Students who failed in both Physics and Chemistry:
Let the number of students who failed in both subjects be x.
Then, according to the given information:
30 + 40 - x = 50
70 - x = 50
x = 20
Therefore, 20 students failed in both Physics and Chemistry.

Probability of passing Physics given that the student failed in Chemistry:
Number of students who failed in Chemistry = 40
Number of students who passed in Chemistry = 100 - 40 = 60
Number of students who passed in both Physics and Chemistry = 100 - 50 = 50
Number of students who passed in Physics but failed in Chemistry = 30 - 20 = 10
Therefore, the probability that a student passed in Physics given that he failed in Chemistry is:
P(passed in Physics | failed in Chemistry) = Number of students passed in Physics and failed in Chemistry / Number of students failed in Chemistry
= 10 / 40
= 1/4
Therefore, the correct answer is:
(c) 1/4
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For a group of students, 30%, 40% and 50% failed in Physics, Chemistry and at least one of the two subjects respectively. If an examinee is selected at random, what is the probability that he passed in physics if it is known that he failed in Chemistry? (a) 1/2 (b) 1/3 (c) 1/4 (d) 1/6?
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For a group of students, 30%, 40% and 50% failed in Physics, Chemistry and at least one of the two subjects respectively. If an examinee is selected at random, what is the probability that he passed in physics if it is known that he failed in Chemistry? (a) 1/2 (b) 1/3 (c) 1/4 (d) 1/6? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about For a group of students, 30%, 40% and 50% failed in Physics, Chemistry and at least one of the two subjects respectively. If an examinee is selected at random, what is the probability that he passed in physics if it is known that he failed in Chemistry? (a) 1/2 (b) 1/3 (c) 1/4 (d) 1/6? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a group of students, 30%, 40% and 50% failed in Physics, Chemistry and at least one of the two subjects respectively. If an examinee is selected at random, what is the probability that he passed in physics if it is known that he failed in Chemistry? (a) 1/2 (b) 1/3 (c) 1/4 (d) 1/6?.
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