Question

Consider randomly selecting a single individual and ha ving that person test drive 3 different v Al-likes vehicle #1 A,-likes vehicle #2 suppose that mA1)-045. pA2)-0.65·RA)" 0.70,阀A, UA2) _ 0.80. mA2na3)-0.40, and (a) what is the probability that the individual likes both vehicle #1 and vehicle #2 4, UA2 UA3)-0.84. (b) Determine PA2 I A). (Round your answer to four decimal places.) Interpret PlAZ IA) r a person likes vehicle #2, this is the probability he or she will also like vehicle #3 This is the probability a person does not like both vehicle #2 and vehicle # 3. This is the probability a person likes both vehicle #2 and vehicle # 3. If a person likes vehicle # 3, this is the probability he or she will also like vehicle #2 @ @ (c) Are A2 and A, independent events? Answer in two different ways. (Select all that apply.) No. PA2 IA) PA2). Therefore A2 and A, are not independent. a No. P(A2 I A) PA2). Therefore, A2 and A, are not independent. m No. Р[A2 n A3) , P(Az)P(A). Therefore, A2 and A3 are not independent. Yes. PA2 nA) PA2)P(A). Therefore, A2 and A are independent. Yes. PIA2 I A) PA). Therefore, A2 and A, are independent Yes. PA2 I A3)-MA2). Therefore, A2 and A3 are independent. ■

Answer 1

a)

P(A1 n A2)=P(A1)+P(A2)-P(A1 u A2)=0.45+0.65-0.80=0.3

b)P(A2|A3)=P(A2 n A3)/P(A3)=0.4/0.7=0.5714

if a person likes vehicle #3 ; this is the probability that he or she will also like vehicle #2

c)

No P(A2|A3) $\neq$ P(A2) therefore A2 and A3 are not independent

No P(A2 n A3) $\neq$ P(A2)*P(A3) therefore A2 and A3 are not independent

d)

P(A2 u A3|A1^c)=(0.84-0.45)/(1-0.45)=0.7091