Question

Suppose that in a certain school the probability that a student studies Chinese is 0.22, the probability that a student studies French is 0.35, and the probability that a student studies both languages is 0.14. Find the probability that a student in that school studies:
a) at least one of these languages
b) exactly one of these languages.

Answer 1

a) To find the probability that a student studies at least one of these languages, we need to find the probability of the union of the two events: studying Chinese and studying French. We can use the formula:

P(Chinese or French) = P(Chinese) + P(French) - P(Chinese and French)

Substituting the given probabilities, we get:

P(Chinese or French) = 0.22 + 0.35 - 0.14 = 0.43

Therefore, the probability that a student in that school studies at least one of these languages is 0.43.

b) To find the probability that a student studies exactly one of these languages, we need to subtract the probability of studying both languages from the probability of studying at least one language. That is:

P(exactly one language) = P(Chinese or French) - P(Chinese and French)

Substituting the given probabilities, we get:

P(exactly one language) = 0.43 - 0.14 = 0.29

Therefore, the probability that a student in that school studies exactly one of these languages is 0.29.