Question

Canada has two official languages: English and French. Choose a Canadian at random and ask "What is your mother tongue?” Here is the distribution of responses, combining many separate languages from the province of Quebec: Language Probability English | French | Other 0.0830.789 ? (a) What is the probability that a Canadian's mother tongue is either English or French? (b) What probability should replace "?" in the distribution? (c) What is the probability that a Canadian's mother tongue is not English?

Answer 1

(a)

Probability that Canadian's mother tongue is either English or French

= Probability that Canadian's mother tongue is English + Probability that Canadian's mother tongue is French

= 0.083+0.789 = 0.872

Probability that Canadian's mother tongue is either English or French = 0.872

(b)

Probability should replace "?" in the distribution

For the given distribution to be a valid , the sum of all probabilities to be equal to 1

i.e.

Probability that Canadian's mother tongue is English + Probability that Canadian's mother tongue is French + Probability that Canadian's mother tongue is other (?) = 1

0.083+0.789 + ? = 1

0.872 + ? = 1

? = 1 - 0.872 = 0.128

? to be replaced by 0.128 in the distribution

(c)

Probability that Canadian's mother tongue is not English

= 1 - Probability that Canadian's mother tongue is English

= 1-0.083=0.917

Probability that Canadian's mother tongue is not English =0.917