Probability of Meeting Italian Who Speaks English in Italy

[Dr-NiKoN]

1 out of 5 italians speak english. 1 out of 5 people in italy are tourists. 1 out 2 tourists speaks english.

You meet a english-speaking person in italy, what is the probability that this person is italian.

The way I see the "population":

$P(I) = \frac{2}{10}$ are italians who speaks english.

$P(T) = \frac{1}{10}$ are tourists that speaks english.

You have meet someone from P(I) + P(T), what is the probability that this person is italian?

That probability equates to:
2x + 1y = 1 (x => english-speaking italian, y => english speaking tourist)

Where do I go from here?

 

[mathman]

Your P(I) is wrong. It should be 4/5(italians) x 1/5 (speak English).
Net result P(I)=.16, P(T)=.1.
P(E) (english speaking)=.26. Your answer is P(I)/P(E).

 

[tacman]

To solve this, we can use the concept of conditional probability. We want to find the probability of meeting an Italian given that the person speaks English. This can be represented as P(I|E).

Using the formula for conditional probability, we have:

P(I|E) = P(I ∩ E) / P(E)

P(I ∩ E) represents the intersection of the two events, which is the probability of meeting an Italian who also speaks English. From the given information, we know that P(I ∩ E) = 2/10.

P(E) represents the probability of meeting someone who speaks English, which is the sum of P(I) and P(T). So we have P(E) = 2/10 + 1/10 = 3/10.

Substituting these values into the formula, we get:

P(I|E) = (2/10) / (3/10) = 2/3

Therefore, the probability of meeting an Italian who speaks English in Italy is 2/3 or approximately 66.67%. This is a relatively high probability, which makes sense given the information provided.