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%.

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

P (M∩CS) = 0.10

Step-by-step 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