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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
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
For a group of students, 30 %, 40% and 50% failed in Physics , Chemist...
Let the total number of students = 100
Number of students failed in physics = 30% of 100 =30
Number of students failed in chemistry = 40% of 100 =40
Number of students failed at least one of the two subjects = 50% of 100 =50
We need to calculate
Most Upvoted Answer
For a group of students, 30 %, 40% and 50% failed in Physics , Chemist...
Given:
- 30% of students failed in Physics
- 40% of students failed in Chemistry
- 50% of students failed in at least one of the two subjects
We need to find the probability that a student passed in Physics given that he failed in Chemistry.
Let's first find the percentage of students who failed in both Physics and Chemistry. We can do this by subtracting the percentage of students who passed in both subjects from 100%:
100% - 50% = 50%
So, 50% of students failed in at least one subject but not both.
Now, we know that the student we are selecting at random failed in Chemistry. This means that the student falls into one of two categories:
1. Failed in both Physics and Chemistry
2. Failed in Chemistry but passed in Physics
We want to find the probability of the second category. We can use conditional probability to do this:
P(passed in Physics | failed in Chemistry) = P(passed in Physics and failed in Chemistry) / P(failed in Chemistry)
We know that P(failed in Chemistry) = 40%. Let's find P(passed in Physics and failed in Chemistry):
P(passed in Physics and failed in Chemistry) = P(failed in both) + P(passed in Physics and failed in Chemistry but not in Physics)
We know that P(failed in both) = 50%, so we just need to find P(passed in Physics and failed in Chemistry but not in Physics):
P(passed in Physics and failed in Chemistry but not in Physics) = P(failed in Chemistry) - P(failed in both) - P(passed in both)
We know that P(passed in both) = 100% - 50% = 50%, so we can substitute the values and solve:
P(passed in Physics and failed in Chemistry but not in Physics) = 40% - 50% - 50% = -60%
Wait, that's not possible! This means that there is no student who failed in Chemistry but passed in Physics.
Therefore, the probability of a student passing in Physics given that he failed in Chemistry is 0/40% = 0, which is equivalent to saying that it is impossible.
The correct answer is none of the options given.
- 30% of students failed in Physics
- 40% of students failed in Chemistry
- 50% of students failed in at least one of the two subjects
We need to find the probability that a student passed in Physics given that he failed in Chemistry.
Let's first find the percentage of students who failed in both Physics and Chemistry. We can do this by subtracting the percentage of students who passed in both subjects from 100%:
100% - 50% = 50%
So, 50% of students failed in at least one subject but not both.
Now, we know that the student we are selecting at random failed in Chemistry. This means that the student falls into one of two categories:
1. Failed in both Physics and Chemistry
2. Failed in Chemistry but passed in Physics
We want to find the probability of the second category. We can use conditional probability to do this:
P(passed in Physics | failed in Chemistry) = P(passed in Physics and failed in Chemistry) / P(failed in Chemistry)
We know that P(failed in Chemistry) = 40%. Let's find P(passed in Physics and failed in Chemistry):
P(passed in Physics and failed in Chemistry) = P(failed in both) + P(passed in Physics and failed in Chemistry but not in Physics)
We know that P(failed in both) = 50%, so we just need to find P(passed in Physics and failed in Chemistry but not in Physics):
P(passed in Physics and failed in Chemistry but not in Physics) = P(failed in Chemistry) - P(failed in both) - P(passed in both)
We know that P(passed in both) = 100% - 50% = 50%, so we can substitute the values and solve:
P(passed in Physics and failed in Chemistry but not in Physics) = 40% - 50% - 50% = -60%
Wait, that's not possible! This means that there is no student who failed in Chemistry but passed in Physics.
Therefore, the probability of a student passing in Physics given that he failed in Chemistry is 0/40% = 0, which is equivalent to saying that it is impossible.
The correct answer is none of the options given.
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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)1/2b)1/3c)1/4d)1/6Correct answer is option 'D'. Can you explain this answer?
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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)1/2b)1/3c)1/4d)1/6Correct answer is option 'D'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation 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)1/2b)1/3c)1/4d)1/6Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 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)1/2b)1/3c)1/4d)1/6Correct answer is option 'D'. Can you explain this answer?.
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