among the 100 fords that a showroom has, 60 are old. it also has a mixed collect

Question

among the 100 fords that a showroom has, 60 are old. it also has a mixed collection of nissans and fiats. the dealer has decided to sell each of the cars at a flat price independent of the model or make. he just chooses a car at random and sell it to the next walking in customer at the flat price. assume that the probability that a new car is chosen given that its a fiat and nissan are .75 and .6 respectively. also the probability that an arbitrarily chosen car is a ford and nissan are 0.2 and 0.4 respectively. now, what is the probability of you getting a ford given that it is a new car.

Explanation / Answer

A: event of getting ford car

B:event of getting fiat car

C:event of getting nissan car

E: event of getting new car

P(B)=0.2

P(C)=0.4

so P(A)= 1-0.4-0.2 = 0.4

P(E/B)=0.75

P(E/C)=0.6

P(E/A)=40/100= 0.4

using bayes theorem

P(A/E) = P(E/A)*P(A) / ( P(E/A)*P(A) + P(E/B)*P(B) + P(E/C)*P(C) )

= 0.4*0.4 / ( 0.4*0.4 + 0.75*0.2 + 0.6*0.4)

=0.2909 (or 16/55)---------------------------------------------------- Answer

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.