Consider the following information about travelers on vacation: 40% check work email, 30% use a cell phone to stay connected to
work, 25% bring a laptop with them, 23% both check work email and use a cell phone to stay connected, and 50% neither check work email nor use a cell phone to stay connected nor bring a laptop. In addition, 84 out of every 100 who bring a laptop also check work email, and 70 out of every 100 who use a cell phone to stay connected also bring a laptop. (a) What is the probability that a randomly selected traveler who checks work email also uses a cell phone to stay connected? (b) What is the probability that someone who brings a laptop on vacation also uses a cell phone to stay connected? (c) If the randomly selected traveler checked work email and brought a laptop, what is the probability that he/she uses a cell phone to stay connected? (Round your answer to four decimal places.)
1 answer:
Answer:
a) 23/40 = 0.575 = 57.5%
b) 21/25 = 0.84 = 84%
c) 20/21 = 0.9524 = 95.24%
Step-by-step explanation:
A - 40% check work email
B - 30% use a cell phone to stay connected to work
C - 25% bring a laptop with them
A and B - 23% both check work email and use a cell phone to stay connected
Not A, B or C - 50% neither check work email nor use a cell phone to stay connected nor bring a laptop.
84% who bring a laptop also check work email
70% who use a cell phone to stay connected also bring a laptop
Consider a population of 100 to facilitate, so:
A = 40
B = 30
C = 25
A and B = 23
Not A, B or C = 50
84% of 25 = 21 ∴ A and C = 21
70% of 30 = 21 ∴ B and C = 21
A, B and C = x
Check picture:
z = 40 - (21-x) - (23-x) = -4+x
w = 30 - (21-x) - (23-x) = -14+x
y = 25 - (21-x) - (21-x) = -17+x
-4+x+23-x+x+21-x-14+x+21-x-17+x+50 = 100
x + 30 = 50
x = 20
Check picture for complete diagram:
(a) What is the probability that a randomly selected traveler who checks work email also uses a cell phone to stay connected?
23/40 = 0.575 = 57.5%
(b) What is the probability that someone who brings a laptop on vacation also uses a cell phone to stay connected?
21/25 = 0.84 = 84%
(c) If the randomly selected traveler checked work email and brought a laptop, what is the probability that he/she uses a cell phone to stay connected?
20/21 = 0.9524 = 95.24%
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