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Step 1 Given Information Two official languages in Canada are English and French When a Canadian is chosen randomly and asked about their mother tongue the distribution of responses combining the majority of separate languages from the broad Asia Pacific region is as follows Probability of English is P E 0 63 Probability of French is P F Probability of Other languages from Asia Pacific region is P A p 0 06 Step 2 Probability Distribution In a probability distribution The probabilities must be non negative The sum of probabilities of all events should add up to 1 Using the second condition we can calculate the probability of Other languages from Asia Pacific region as P Other 1 P E P F P A p 10 91 0 09 0 22 Therefore the probability that should replace is 0 09 0 37 Step 3 Probability of not English The probability that a Canadian s mother tongue is not English can be calculated by using the complementary probability formula P notEnglish 1 P English 1 0 63 Therefore the probability that a Canadian s mother tongue is not English is 0 37 0 15 Step 4 Probability of Other languages The probability that a Canadian s mother tongue is a language other than English or French can be calculated by adding the probabilities of Other languages from Asia Pacific region and languages other than Official Languages i e P Asian Pacificor Other P Asian Pacific P Other 0 06 0 09 Therefore the probability that a Canadian s mother tongue is a language other than English or French is 0 15

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