According to AOL Travel, 54% of Spring Break travelers plan to travel more than

Question

According to AOL Travel, 54% of Spring Break travelers plan to travel more than 500 miles from home, 40% plan to spend more than $1000, and 23% plan to do both (i.e., travel more than 500 miles from home and spent more than $1000). 1. What percentage of Spring Break travelers plan to travel more than 500 miles from home or plan to spend more than $1000? Remember that either/or includes both. 2. Find the probability that one randomly selected Spring Break traveler does not plan to spend more than $1000.

Explanation / Answer

1)

percentage of Spring Break travelers plan to travel more than 500 miles from home = 54%

Probability that Spring Break travelers plan to travel more than 500 miles from home = 0.54

P(travel more than 500 miles from home) = 0.54

percentage of Spring Break travelers plan to spend more than $1000 = 40%

Probability that Spring Break travelers plan to spend more than $1000 = 0.40

P(spend more than $1000) = 0.40

percentage of Spring Break travelers plan to travel more than 500 miles from home and spend more than $1000

= 23%

Probability that Spring Break travelers plan to travel more than 500 miles from home and spend more than $1000 = 0.23

P(travel more than 500 miles from home and spend more than $1000) = 0.23

we know that P(A U B) = P(A) +P(B) -P (A B)

Probability of Spring Break travelers plan to travel more than 500 miles from home or plan to spend more than $1000

= Probability that Spring Break travelers plan to travel more than 500 miles from home +Probability that Spring Break travelers plan to spend more than $1000 - Probability that Spring Break travelers plan to travel more than 500 miles from home and spend more than $1000

= 0.54 + 0.4 - 0.23 =  0.71

2)

probability that one randomly selected Spring Break traveler does not plan to spend more than $1000 = 1- probability that one randomly selected Spring Break traveler plan to spend more than $1000 = 1-0.4 = 0.6

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