Question

35% of students take spainsh or engineering. 30% of students take Spanish. 25% of students take engineering. What is the probability that a student takes Spanish and engineering?

Answer 1

0.2 = 20% probability that a student takes Spanish and engineering

Explanation:

We solve this question treating the probabilities as Venn sets.

I am going to say that:

Event A: Student takes Spanish

Event B: Student takes Engineering.

35% of students take spainsh or engineering.

This means that
`P(A \cup B) = 0.35`

30% of students take Spanish.

This means that
`P(A) = 0.3`

25% of students take engineering.

This means that
`P(B) = 0.25`

What is the probability that a student takes Spanish and engineering?

This is
`P(A \cap B)`.

These probabilities are related by the following formula:

`P(A \cup B) = P(A) + P(B) - P(A \cap B)`

So

`P(A \cap B) = P(A) + P(B) - P(A \cup B)`

Replacing the values

`P(A \cap B) = 0.3 + 0.25 - 0.35 = 0.2`

0.2 = 20% probability that a student takes Spanish and engineering