Multiplication Rule: Example 1 In a sample of 150 residents, each person was ask
ID: 3334722 • Letter: M
Question
Multiplication Rule: Example 1 In a sample of 150 residents, each person was asked if he or she favored the concept of a single countywide police agency. The county is composed of one large city and many suburban townships. The residence (city or outside the city) and the responses of the residents are summarized. nion Residence Favor (F) OpposeTotal Outside of city (C) Total 80 20 100 40 10 50 120 30 150 a) If one of these residents was to be selected at random, what is the probability that the person will favor the concept? P (F) b) If one of these residents was to be selected at random, what is the probability that the person will favor the concept if (given that) the person selected is a city resident? P(C) c) If one of these residents was to be selected at random, what is the probability that the person will favor the concept if (given that) the person selected is a resident from outside the CI P(FC)- P(C) d) Two events are said to be independent if the probability if the occurrence of one does not affect the probability of the other event. In other words P(FIC) P (F). Compare your results to above and explain your decision.Explanation / Answer
a) probability that person will favour P(F)=100/150 =2/3 (as there are 100 people who favour out of 150)
b)P(F|C) =P(F n C)/P(C)= 80/120 =2/3
c) P(F|Cc )=P(F n Cc)/P(Cc) =20/30 =2/3
d) as we see that P(F)=P(F|C) =P(F|Cc ) ;therefore event F is not dependent on C or Cc
hence F and C are independent
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