Question

I will rate and comment, please answer all questions below

In a survey of 200 US residents: 150 have traveled to Canada, 120 to Mexico, and 90 have traveled to both countries. What’s the probability that a US resident chosen at random has

a) traveled to Canada but not to Mexico _________________

b) traveled to either Canada or Mexico, but not both ___________

c) traveled to either Canada or Mexico ______________________

d) not traveled to either country ___________________________

e) traveled to Canada or not to Mexico ________________________

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

      (hint: given that they have traveled to Mexico)

         

g) Are traveling to Mexico and Canada disjoint events? Explain

h) Are traveling to Mexico and Canada independent events? Explain using numbers.

Answer 1

Let C shows the event that US resident travel to Canada, M shows the event that US resident travel to Mexico. So we have

P(C) = 150 /200 = 0.75

P(M) = 120 /200 = 0.60

P(M and C) = 90/200= 0.45

a)

The probability that a US resident chosen at random has traveled to Canada but not to Mexico is

P(C and not M) = P(C) - P(M and C) = 0.75 - 0.45= 0.30

b)

The probability that a US resident chosen at random traveled to either Canada or Mexico, but not both is

P(C and not M) +P(M and not C) = [P(C) - P(M and C)]+[P(M)-P(M and C)] = 0.75 - 0.45 + 0.60 - 0.45= 0.45

c)

The probability that a US resident chosen at random has traveled to either Canada or Mexico  is

P(C or M) = P(C) +P(M) - P(M and C) = 0.75+0.60 - 0.45 = 0.90

d)

The probability that a US resident chosen at random has not traveled to either country  is

P(not C and not M) = 1- P(C or M) = 1- 0.90 =0.10

e)

P(C or not M) = P(C) + P(not M) - P(C and not M) = 0.75 + 1 - 0.60 - 0.30 = 0.85

f)

P(C|M) = P(C and M) / P(M) = 0.45 / 0.60 = 0.75

g)

No because P(M and C) is not equal to zero.

h)

Yes because

P(C|M) =P(C)