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In a class, 40% students study Mathematics, 25% study Chemistry and 15% study both the subjects. A student is chosen at random. The probability that he studies Mathematics, if it is known that he studies Chemistry, is
- a)1/8
- b)3/8
- c)2/5
- d)3/5
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
In a class, 40% students study Mathematics, 25% study Chemistry and 15...
Given,
P(M) = 40/100 = 2/5
P(C) = 25/100 = 1/4
P(M ∩ C) = 15/100 = 3/20
P(M/C) = P(M ∩ C)/P(C) = {3/20}/{1/4} = 3/5
P(M) = 40/100 = 2/5
P(C) = 25/100 = 1/4
P(M ∩ C) = 15/100 = 3/20
P(M/C) = P(M ∩ C)/P(C) = {3/20}/{1/4} = 3/5
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Community Answer
In a class, 40% students study Mathematics, 25% study Chemistry and 15...
Understanding the Problem
To find the probability that a student studies Mathematics given that they study Chemistry, we can use the concept of conditional probability.
Given Data
- Percentage of students studying Mathematics: 40%
- Percentage of students studying Chemistry: 25%
- Percentage of students studying both subjects: 15%
Let’s denote:
- P(M) = Probability of studying Mathematics = 0.40
- P(C) = Probability of studying Chemistry = 0.25
- P(M ∩ C) = Probability of studying both Mathematics and Chemistry = 0.15
Conditional Probability Formula
The conditional probability is given by the formula:
P(M | C) = P(M ∩ C) / P(C)
Here, P(M | C) is the probability that a student studies Mathematics given that they study Chemistry.
Calculating Values
1. Substituting the values:
P(M | C) = P(M ∩ C) / P(C)
= 0.15 / 0.25
2. Simplifying the fraction:
= 0.15 ÷ 0.25 = 0.15 * (1/0.25) = 0.15 * 4 = 0.60
Conclusion
Thus, the probability that a student studies Mathematics, given that they study Chemistry, is:
P(M | C) = 0.60 or 3/5.
Hence, the correct answer is option 'D'.
To find the probability that a student studies Mathematics given that they study Chemistry, we can use the concept of conditional probability.
Given Data
- Percentage of students studying Mathematics: 40%
- Percentage of students studying Chemistry: 25%
- Percentage of students studying both subjects: 15%
Let’s denote:
- P(M) = Probability of studying Mathematics = 0.40
- P(C) = Probability of studying Chemistry = 0.25
- P(M ∩ C) = Probability of studying both Mathematics and Chemistry = 0.15
Conditional Probability Formula
The conditional probability is given by the formula:
P(M | C) = P(M ∩ C) / P(C)
Here, P(M | C) is the probability that a student studies Mathematics given that they study Chemistry.
Calculating Values
1. Substituting the values:
P(M | C) = P(M ∩ C) / P(C)
= 0.15 / 0.25
2. Simplifying the fraction:
= 0.15 ÷ 0.25 = 0.15 * (1/0.25) = 0.15 * 4 = 0.60
Conclusion
Thus, the probability that a student studies Mathematics, given that they study Chemistry, is:
P(M | C) = 0.60 or 3/5.
Hence, the correct answer is option 'D'.
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In a class, 40% students study Mathematics, 25% study Chemistry and 15% study both the subjects. A student is chosen at random. The probability that he studies Mathematics, if it is known that he studies Chemistry, isa)1/8b)3/8c)2/5d)3/5Correct answer is option 'D'. Can you explain this answer?
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