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

Answer:

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

Step-by-step 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