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In a class 40 % students read Mathematics, 25 % Biology and 15 % both Mathematics and Biology. One student is select at random.The probability that he reads Biology if he reads Mathematics
- a)7/8
- b)1/8
- c)3/8
- d)none
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
In a class 40 % students read Mathematics, 25 % Biology and 15 % both ...
Solution:
Given,
percentage of students who read Mathematics = 40%
percentage of students who read Biology = 25%
percentage of students who read both Mathematics and Biology = 15%
Let,
M = event that a student reads Mathematics
B = event that a student reads Biology
To find: Probability of reading Biology given that the student reads Mathematics i.e. P(B|M)
We know that,
P(B ∪ M) = P(B) + P(M) - P(B ∩ M) (where ∪ represents union and ∩ represents intersection)
Also,
P(B ∪ M) = 100% (as all students either read Mathematics or Biology or both)
Therefore,
P(B) + P(M) - P(B ∩ M) = 100%
25% + 40% - 15% = 50%
Now, we can use the formula of conditional probability to find P(B|M):
P(B|M) = P(B ∩ M) / P(M)
= 15% / 40%
= 3/8
Hence, the correct option is (c) 3/8.
Given,
percentage of students who read Mathematics = 40%
percentage of students who read Biology = 25%
percentage of students who read both Mathematics and Biology = 15%
Let,
M = event that a student reads Mathematics
B = event that a student reads Biology
To find: Probability of reading Biology given that the student reads Mathematics i.e. P(B|M)
We know that,
P(B ∪ M) = P(B) + P(M) - P(B ∩ M) (where ∪ represents union and ∩ represents intersection)
Also,
P(B ∪ M) = 100% (as all students either read Mathematics or Biology or both)
Therefore,
P(B) + P(M) - P(B ∩ M) = 100%
25% + 40% - 15% = 50%
Now, we can use the formula of conditional probability to find P(B|M):
P(B|M) = P(B ∩ M) / P(M)
= 15% / 40%
= 3/8
Hence, the correct option is (c) 3/8.
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Community Answer
In a class 40 % students read Mathematics, 25 % Biology and 15 % both ...
P(M∩B) = 15
P(M) = 40
P(B) = 25
P(B/M) = [ P(M∩B) ] / P(M)
= 15 / 40
= 3/8
P(M) = 40
P(B) = 25
P(B/M) = [ P(M∩B) ] / P(M)
= 15 / 40
= 3/8
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In a class 40 % students read Mathematics, 25 % Biology and 15 % both Mathematics and Biology. One student is select at random.The probability that he reads Biology if he reads Mathematicsa)7/8b)1/8c)3/8d)noneCorrect answer is option 'C'. Can you explain this answer?
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