Question

At a certain college, 23% of students speak Spanish, 8% speak Italian, and 3% speak both languages. A student is chosen at random from the college. What is the probability that the student speaks Spanish given that he or she speaks Italian?

Answer 1

`P(S/I)=0.375`

Explanation:

Let's start defining the conditional probability of an event :

Given two events A and B :

`P(A/B)=(P(A,B))/(P(B))`

with P(B) > 0

Where P(A/B) is the probability of event A given that event B occur

P(A,B) is the probability of the event in which A and B occur both at the same time.

Let's write the events for our exercise

S : ''A random student speaks Spanish''

I : ''A random student speaks Italian''

`P(S)=0.23\\P(I)=0.08\\P(S,I)=0.03`

Applying the conditional equation we obtain :

`P(S/I)=(P(S,I))/(P(I))=(0.03)/(0.08)=0.375`

Then, 0.375 is the probability that we are looking for