6 A survey of benefits for 254 corporate executives Business

6. A survey of benefits for 254 corporate executives (Business Week, October
24, 1994) showed that 155 executives were provided mobile phones, 152 were
provided club memberships, and 110 were provided both mobile phones and
club memberships as perks associated with their position.
(a) Let M be the event of having a mobile phone and C be the event of having a
club membership. Find the following probabilities: P (M ), P (C ), and
P (M C ).
(b) Use the probabilities in part (a) to compute the probability that a corporate
executive has at least one of the two perks.
(c) What is the probability that a corporate executive does not have either
of these perks.
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(d) Organize the probabilistic information into a probability tree whose first
stage represents ownership of a mobile phone, and whose second stage
represents enrollment in club membership.
(e) Determine the probability that a corporate executive does not have club
membership given that that executive has a mobile phone.
(f ) Determine the probability that a corporate executive does not have a
mobile phone given that that executive does not have club membership.

Solution

155 MOBILE PHONES. 152 MEMBERSHIP AND 110 BOTH

WHICH MEANS 45 PPL WERE GIVEN ONLY MOBILE PHONES AND 42 PEOPLE WERE GIVEN ONLY MEMBERSHIP AND 110 WERE GIVEN BOTH. TOTAL 197 WERE GIVEN SOMETHING, THEREFORE 57 PEOPLE WERE NOT GIVEN ANYTHING

A)P(M) = 155/254

P(C)=152/254

P(M INTERSECTION C ) = 110/254

B)P( HAVING ATLEST ONE MEANS.) = 197/254

C) P(DONT HAVE ANY PERK) = 57/254

E) P(HAVING MOBILE NOT MEMBERSHIP) =(45+57)/155

F) P(HAVING NOTHING) = 57/152