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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 Mathematics if it is known that he reads Biology is
- a)2/5
- b)3/5
- c)4/5
- d)none
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In a class 40 % students read Mathematics, 25 % Biology and 15 % both ...
Given information:
- 40% of students read Mathematics.
- 25% of students read Biology.
- 15% of students read both Mathematics and Biology.
To find:
- The probability that a student reads Mathematics if it is known that he reads Biology.
Solution:
Step 1: Draw a Venn diagram representing the given information.
The rectangle represents the total number of students in the class. The circle on the left represents the number of students who read Mathematics, and the circle on the right represents the number of students who read Biology. The overlapping region represents the number of students who read both Mathematics and Biology.
Step 2: Calculate the number of students who read only Biology.
To do this, we subtract the number of students who read both Mathematics and Biology from the total number of students who read Biology.
Number of students who read only Biology = Total number of students who read Biology - Number of students who read both Mathematics and Biology
= 25% - 15%
= 10%
Step 3: Calculate the probability that a student reads Mathematics given that he reads Biology.
We can use Bayes' theorem to calculate this probability.
P(Mathematics | Biology) = P(Biology | Mathematics) * P(Mathematics) / P(Biology)
- P(Mathematics) = 40%
- P(Biology) = 25%
- P(Biology | Mathematics) = The probability that a student reads Biology given that he reads Mathematics. This can be calculated as follows:
P(Biology | Mathematics) = (Number of students who read both Mathematics and Biology) / (Total number of students who read Mathematics)
= 15% / 40%
= 3/8
Substituting these values into Bayes' theorem, we get:
P(Mathematics | Biology) = (3/8 * 40%) / 25%
= 3/5
Therefore, the probability that a student reads Mathematics given that he reads Biology is 3/5 or option B.
- 40% of students read Mathematics.
- 25% of students read Biology.
- 15% of students read both Mathematics and Biology.
To find:
- The probability that a student reads Mathematics if it is known that he reads Biology.
Solution:
Step 1: Draw a Venn diagram representing the given information.
The rectangle represents the total number of students in the class. The circle on the left represents the number of students who read Mathematics, and the circle on the right represents the number of students who read Biology. The overlapping region represents the number of students who read both Mathematics and Biology.
Step 2: Calculate the number of students who read only Biology.
To do this, we subtract the number of students who read both Mathematics and Biology from the total number of students who read Biology.
Number of students who read only Biology = Total number of students who read Biology - Number of students who read both Mathematics and Biology
= 25% - 15%
= 10%
Step 3: Calculate the probability that a student reads Mathematics given that he reads Biology.
We can use Bayes' theorem to calculate this probability.
P(Mathematics | Biology) = P(Biology | Mathematics) * P(Mathematics) / P(Biology)
- P(Mathematics) = 40%
- P(Biology) = 25%
- P(Biology | Mathematics) = The probability that a student reads Biology given that he reads Mathematics. This can be calculated as follows:
P(Biology | Mathematics) = (Number of students who read both Mathematics and Biology) / (Total number of students who read Mathematics)
= 15% / 40%
= 3/8
Substituting these values into Bayes' theorem, we get:
P(Mathematics | Biology) = (3/8 * 40%) / 25%
= 3/5
Therefore, the probability that a student reads Mathematics given that he reads Biology is 3/5 or option B.
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Community Answer
In a class 40 % students read Mathematics, 25 % Biology and 15 % both ...
P(M and B) =15/100
P(B) =25/100
P(M/B) =P(M and B) /P(B)
=0.15/0.25
=3/5
P(B) =25/100
P(M/B) =P(M and B) /P(B)
=0.15/0.25
=3/5
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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 Mathematics if it is known that he reads Biology isa)2/5b)3/5c)4/5d)noneCorrect answer is option 'B'. Can you explain this answer?
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