Question

Iven that, in a certain school, the following are true, what is the probability that a student is taking both math and computer science?

1. The probability that a student is taking math is 23%.
2. The probability that a student is taking computer science is 45%.
3. The probability that a student is taking math or computer science is 58%.

Answer 1

The probability that a student is taking both math and computer science

P(M∩CS) = 0.10

Explanation:

Explanation:-

Given data the probability that a student is taking math is 23%

Let 'M' be the event of a student is taking math

P(M) = 0.23

Let 'CS' be the event of a student is taking computer science

Given data the probability that a student is taking computer science is 45%

P(CS) = 0.45

Given the probability that a student is taking math or computer science is 58%.

P(M U CS) = 0.58

Addition theorem on probability

If S is a sample size , and E₁ and E₂ be the events in S then

P(E₁ or E₂ ) = P(E₁) + P(E₂) - P(E₁ and E₂)

or

P(E₁ ∪E₂ ) = P(E₁) + P(E₂) - P(E₁ ∩ E₂)

Now

P(M∪ CS ) = P(M) + P(CS) - P(M∩CS)

0.58 = 0.23 + 0.45 - P(M∩CS)

P(M∩CS) = 0.68 -0.58

P(M∩CS) = 0.10

Conclusion:-

The probability that a student is taking both math and computer science

P(M∩CS) = 0.10