Canada has two official languages: English and French. Choose a Canadian at rand

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:4

Language - English French Other

Probability - 0.083 0.789 ?

(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?

Below is the way they would like the question answered. Please follow the Rule below to answer the question above with showing work.

Rule 1. The probability P (A) of any event A satisfies 0 P(A) 1.

Rule 2. If S is the sample space in a probability model, then P (S) = 1.

Rule 3. Two events A and B are disjoint if they have no outcomes in common and so can never occur together. If A and B are disjoint,

P (A or B) = P(A) + P(B)

This is the addition rule for disjoint events.

Rule 4. For any event A,

P(A does not occur) = 1 – P(A)

The addition rule extends to more than two events that are disjoint in the sense that no two have any outcomes in common. If events A, B, and C are disjoint, the probability that one of these events occurs is P(A) + P(B) + P(C).

Explanation / Answer

Ans:

a)As all events are disjoint,so

P(English or French)=P(English)+P(French)

=0.083+0.789

=0.872

b)P(other)=1-0.083-0.789=1-0.872=0.128

c)P(not English)=P(French)+P(other)=0.789+0.128=0.917

or

P(not English)=1-P(English)=1-0.083=0.917

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.