Question

A group of friends have been surveyed. 38% have been to Canada. 80% have been to France. 11% have been to neither Canada or France. Find the percentage of the group that have been to Canada and France.​

Answer 1

38 + 80 - x = 118 - x

But we know that 11% have been to neither country, which means that:

100 - 11 = 89 people have been to at least one of the countries.

Therefore, 118 - x = 89x = 29

So, 29 people have been to both Canada and France.
Therefore, the percentage of the group that have been to Canada and France is:

29%

Answer 2

Answer: 29%

Explanation:

Let's use the formula of the Inclusion-Exclusion Principle to find the percentage of the group that have been to both Canada and France:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

In this case, A represents the people who have been to Canada, B represents the people who have been to France, and A ∩ B represents the people who have been to both Canada and France.

We are given:

P(A) = 0.38 (38% have been to Canada)

P(B) = 0.80 (80% have been to France)

P(A ∪ B) = 1 - P(neither) = 1 - 0.11 = 0.89 (since 11% have been to neither Canada or France, 89% have been to at least one of them)

Now, we can find the percentage of the group that have been to both Canada and France (P(A ∩ B)):

0.89 = 0.38 + 0.80 - P(A ∩ B)

P(A ∩ B) = 0.38 + 0.80 - 0.89

P(A ∩ B) = 1.18 - 0.89

P(A ∩ B) = 0.29

So, 29% of the group have been to both Canada and France.