Question

Problem #5 For each part of this problem, show calculations or identify where/how you obtained your numerical answer. It may be helpful to draw a diagram. **Give your final answer written as a probability statement.**

Suppose the probability that a U.S. resident has traveled to Canada is 0.18, to Mexico is 0.09, and has traveled to both countries is 0.04. What is the probability that an American chosen at random …

a) …has traveled to Canada but not Mexico?

b) …has traveled to either Canada or Mexico?

c) …has not traveled to either country?

d) What is the probability that someone who has traveled to Mexico has also visited Canada?

e) Are having traveled to Mexico and having traveled to Canada disjoint events? Explain.

f) Are having traveled to Mexico and having traveled Canada independent events? Explain.

Answer 1

Let us write A and B as the events denoting that an American resident has traveled to Canada and Mexico respectively.

Given,

Part a

Required probability =

Part b

Required probability =

Part c

Required probability =

Part d

Required probability =

Part e

Travelling to Mexico and travelling to Canada are not disjoint, since one can visit to both countries, and indeed that has a positive probability of 0.04.

Part f

Note that,

Hence, travelling to Mexico and travelling to Canada are not independent.