Exercise 3.3 (TRUCK LOVERS) A survey 00 + DGC-.248 families in a city of automob

Question

Exercise 3.3 (TRUCK LOVERS) A survey 00 + DGC-.248 families in a city of automobile ownership was conducted for of o States and particular city. The results of the study showing o aid foreign manufacturers are given below: Do you own a U.S. Truck? esNo 120 30 Do you own a foreign Truck? Yes No 110 Fig. 3.3. Trucks (a ) Complete the above Table. (b ) What is the probability that a randomly selected family will own trucks? Cc) What is the probability that a randomly selected family will not own trucks? both U.S. and Foreign (d) What is the probability that a randomly selected family will not own a U.S, truck own a Foreign truck? but will Ce) What is the probability that a randomly selected family will own a U.S. truck, but not a Foreign truck? (f) Given that a randomly selected family owns a U.S, truck, what is the probability that will also own a foreign truck? (g) Given that a randomly selected family owns a U.S. truck, what is the probability that they will not own a foreign truck? (h) Given that a randomly selected family owns a Foreign truck, what is the probability they will also own a U.S. truck? (i) Given that a randomly selected family owns a Foreign truck, what is the probability that they will not own a U.S. truck? (j) Are the events "Own a US. truck" and "Own a foreign truck" independent? Justfy your claim.

Explanation / Answer

a) let the unknown value be x

120+ 30+110+ x = 200 + DGC = 248

260+x = 248

x = -12

hence not possible , it is due to low value of DGC

i am going to answer in terms of x

b)

A - foreign truck , B- US truck

P(A and B) = 120/(260+ x)

c)

1- P(A and B) = (140+x)/(260+x)

d)

30/(260+x)

e) 110/(260+x)

f) P(A|B) = 120/230

g) 110/230

h) 120/(120+30) = 4/5

i)30/150 = 1/5

j) P(A) = 150/(260+x)

P(B) = 230/(260+x)

P(A and B ) = 120/(260+x)

if P(A and B) = P(A) P(B)

then A and B are independent

most probably it will be not be independent

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