Question

Languages in Canada 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 broad Asia/Pacific region:$6$Language: English French Asian/Pacific Other Probability: $0.630.220.06$?

(a) What probability should replace “?” in the distribution? Why?

(b) What is the probability that a Canadian’s mother tongue is not English?

(c) What is the probability that a Canadian’s mother tongue is a language other than English or French?

Short answer

Part (a) The probability of other $=0.09$

Part (b) The probability of not English=$0.37$

Part (c) The probability is$0.15$

Step-by-step solution

Part (a)  Step 1. Given Information 

The likelihood of English, $P\left(E\right)=0.63$

The likelihood of French, $P\left(F\right)=0.22$

The likelihood of Asian/Pacific, $P\left(\raisebox{1ex}{$A$}\!\left/ \!\raisebox{-1ex}{$P$}\right.\right)=0.06$

Part (a) Step 2. Concept Used  

An event is a subset of an experiment's total number of outcomes. The ratio of the number of elements in an event to the number of total outcomes is the probability of that occurrence.

Part (a)  Step 3. Calculation   

The following are the conditions for probability distribution: 1) The probabilities must be

2)The sum of all probability should equal $1$. Using condition $2$, $$\begin{gathered} 0.63+0.22+0.06+P\left(other\right)=1 \\ P\left(Other\right)=1-0.91=0.09 \end{gathered}$$

Part (b) Step 1. Calculation   

$P(A^c)=1-P\left(A\right)$Using the complementary probability formula,$P(notEnglish)=1-P\left(English\right)=1-0.63=0.37$

Part (c) Step 1. Calculation  

$P(AorB)=P\left(A\right)+P\left(B\right)$The likelihood that a Canadian's mother tongue language is neither English or French denotes the Asian/Pacific or Other language. By applying a formula,$P(Asian/PacificorOther)=P(Asian/Pacific)+P\left(Other\right)P(Asian/PacificorOther)=0.06+0.09=0.15$