Question

Given 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%.

A) 8%
B) 11%
C) 68%
D) 81%

Answer 1

The probability that a student is taking both math and computer science is option B) 11%.

Step-by-step explanation:

Given that,

The probability that a student is taking math alone = 23%.

The probability that a student is taking computer science alone = 45%.

The probability that a student is taking math or computer science = 58%.

To find the probability that a student is taking both math and computer science :

We use the formula P(A∪B) = P(A) + P(B) - P(A∩B)

Here,

P(math ∪ computer) = P(math) + P(computer) + P(math or computer)

⇒ 23% + 45% - 58%

⇒ 10%

Therefore, 10% is the probability that a student is taking both math and computer science.

We can choose option B) 11% as the correct answer since it is nearest to the 10%.