Question

1

. Given a sample of 1000 persons, 500 from group A; 500 from group B. (25 Points) 85% of group A have characteristic 1 and 62% of group B have characteristic 1. a) Construct a contingency table based on totals with the two groups and characteristic 1 and not(characteristic 1) as entries. b) Give an example of a simple event and a joint event? c) What is the probability that a randomly selected person has characteristic 1? d) What is the probability that a randomly selected person has characteristic 1 and is in group B? e) Are group and characteristic 1 independent? f) What is the probability of being in group B and not possessing characteristic 1?

Answer 1

from above:

		not
	have char 1	have char 1	total
group A	425	75	500
group B	310	190	500
total	735	265	1000

b)

simple event :having a person from group A

joint event: having a person from group A who have cahrecteristic 1

c)

probability that a randomly selected person has characteristic 1 =735/1000=0.735

d)

probability that a randomly selected person has characteristic 1 and is in group B =310/1000 =0.31

e)

No as P( characteristic 1 and is in group B) =0.31 is not equal to P(characteristic 1)*P( group B)=0.735*0.5=0.3675

f)

probability of being in group B and not possessing characteristic 1 =190/1000 =0.19