9. In a study of honeymoon vacations for newlyweds in the United States, it was

Question

9. In a study of honeymoon vacations for newlyweds in the United States, it was determined that 79% take place outside of the country, 64% last longer than 7 days, and 50% are both outside the country and last longer than 7 days. Find the following probabilities: (a) What is the probability that a honeymoon vacation takes place outside of the country or lasts longer than 7 days? (b) What is the probability that a honeymoon vacation lasts longer than 7 days given that it takes place outside of the country? moon vacation takes place of the country given that it does not last longer than 7 days?

Explanation / Answer

a) P(honeymoon outside the country and last longer than 7 days)

= 0.79+0.64-0.50

= 0.93

b) P( last longer than 7 days/honeymoon outside the country)

= 0.50/0.79

= 0.6329

c) P(honeymoon outside the country/not last less longer than 7 days)

= P(honeymoon outside the countr and not last less longer than 7 days) =0.79-0.50 = 0.29

P(honeymoon outside the country/not last less longer than 7 days) = 0.29/(1-0.64)

= 0.8056

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