Consider the following information about travelers on vacation: 40% check work e

Question

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, 19% both check work email and use a cell phone to stay connected, and 51% 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?    Incorrect: Your answer is incorrect. (b) What is the probability that someone who brings a laptop on vacation also uses a cell phone to stay connected?    Incorrect: Your answer is incorrect. (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.) 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, 19% both check work email and use a cell phone to stay connected, and 51% 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?    Incorrect: Your answer is incorrect. (b) What is the probability that someone who brings a laptop on vacation also uses a cell phone to stay connected?    Incorrect: Your answer is incorrect. (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.) 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, 19% both check work email and use a cell phone to stay connected, and 51% 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?    Incorrect: Your answer is incorrect. (b) What is the probability that someone who brings a laptop on vacation also uses a cell phone to stay connected?    Incorrect: Your answer is incorrect. (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.)

Explanation / Answer

let probability of chck work email =P(E) =0.40 ; cell phone =P(C) =0.30 ; using laptop =P(L) =0.25

P(C & E) =0.19 ;

P(Ec & Cc & Lc) =0.51

1-P(E U C U L) =0.51

P(E U C U L) =0.49

also P(E|L) =0.84

P(L|C) =0.70

from above informationL

a) probability that a randomly selected traveler who checks work email also uses a cell phone to stay connected

=P(E & C)/P(E) =0.19/0.40=19/40 =0.475

b)probability that someone who brings a laptop on vacation also uses a cell phone to stay connected

=P(C|L) =P(C)*P(L|C)/P(L) =0.3*0.70/0.25=21/25 =0.84

c)here probabilityof using all of them P(E & L & C)=P(E U C U L) +P(E &C)+P(E & L)+P(C &L) -P(E)-P(C)-P(L)

P(E & L & C) =0.49+0.19+0.3*0.7+0.25*0.84-0.40-0.30-0.25=0.15

probability that he/she uses a cell phone to stay connected given checked work email and brought a laptop

=P(C|E & L) =P(C & L & E)/P( L & E) =0.15/0.21 =0.7143

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