A certain company has two car assembly plants, A and B. Plant A produces twiceas many cars as plant B. Plant A uses engines and transmissions from a subsidiaryplant which produces 10% defective engines and 2% defectivetransmissions. Plant B uses engines and transmissions from another source where8% of the engines and 4% of the transmissions are defective. Car transmissionsand engines at each plant are installed independently. a) What is the probability that a car chosen at random will have a good engine?
b) What is the probability that a car from plant A has a defective engine, or adefective transmission, or both?
c) What is the probability that a car which has a good transmission and adefective engine was assembled at plant B?

1/6

step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

7 is the median   7.875 is the mean

step-by-step explanation:

3,4,5,6,8,11,13,13