Question

Consider the following information about passengers on a cruise ship on vacation: 41% check work e-mail, 29% use bring a laptop with them on vacation, 22% both check work e-mail and use a cell phone to stay connected, and 50% neither check work e-mail nor use a cell phone to stay connected nor bring a laptop. In addition 88% of those who bring a laptop also check work e-mail and 71% of those who use a cell phone to stay connected also bring a laptop. With cell phone to stay connected to work, 26% E = event that a traveler on vacation checks work e-mail C event that a traveler on vacation uses a cell phone to stay connected event that a traveler on vacation brought a laptop L use the given information to determine the following probabilities. A Venn diagram may help. (Round all answers to four decimal places.) (a) P(E) (b) P(C) (c) P(L) (d) P(E and C) = P(EC and c and LC) (e) (f) P(E or C or L) (9) P(EIL) (h) P(LIC) = P(E and C and L) (i) P(E and L) (J) P(C and L) (k) (I) P(CI(E and L)) =

Answer 1

(a)

P(E) = P(a traveler on vacation checks work e-mail)

= 0.4100 [Answer] (It is given in question that 41% travelers check work e-mail)

(b)

P(C) = P(a traveler on vacation uses a cell phone to stay connected)

= 0.2900 [Answer] (It is given in question that 29% travelers use a cell phone)

(c)

P(L) = P(a traveler on vacation brought a laptop)

= 0.2600 [Answer] (It is given in question that 26% travelers brought a laptop)

(d)

P(E and C)P(EnC) P(a traveller on vacation both checks work e-mail and uses a cell phone) [Answer - 0.2200
(It is given in question that 22% both check work e-mail and use a cell phone)

(e)

P(EC and C and L)= P(E c nL) - P(a traveller on vacation neither checks work e-mail nor laptop) cell phone nor brings uses a a [Answer] 0.5000

(It is given in question that 50% neither check work e-mail nor use a cell phone nor bring a laptop)

(f)

P(E or C or L) P(EUCUL) 1 P((EUCU L)C) 1 P(ECncnL - 1- 0.5000 [Using De Morgan's Law] Answer] 0.5000

(g)

P(EL 0.8800 Answer

(It is given in question that 88% of those who bring a laptop also check work e-mail)

(h)

P(L|C) = 0.7100 [Answer]   (It is given in question that 71% of those who use a cell phone to stay connected also bring a laptop)

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