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I am Lyosha [343]
3 years ago
6

In a study of honeymoon vacations for newlyweds in the United States, it was determined that 79% take place outside of the count

ry, 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? (c) What is the probability that a honeymoon vacation takes place outside of the country given that it does not last longer than 7 days?
Mathematics
1 answer:
Ivanshal [37]3 years ago
5 0

Answer:

Step-by-step explanation:

Given that 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.

Let A - honey moon outside country

B - last longer than 7 days

Then P(A) = 0.79\\P(B) = 0.64\\P(AB) = 0.50

a)  the probability that a honeymoon vacation takes place outside of the country or lasts longer than 7 days

=P(AUB) = P(A)+P(B)-P(AB)\\= 0.79+0.64-0.50\\=0.93

b) the probability that a honeymoon vacation lasts longer than 7 days given that it takes place outside of the country

=P(B/A) = \frac{P(AB)}{P(A)} \\=\frac{0.50}{0.79} =0.6329

c) the probability that a honeymoon vacation takes place outside of the country given that it does not last longer than 7 days

=P(B/A') = \frac{P(A'B)}{P(A')} =\frac{P(B)-P(AB)}{1-P(A)} \\=\frac{0.64-0.5}{1-0.79} \\=0.6667

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