A firm makes couches in four different styles and three different fabrics, as in

Question

A firm makes couches in four different styles and three different fabrics, as indicated in the following table. Use this information to answer the questions that follow.

a). Calculate the probability that a couch picked at random will be made from fabric 1.

b). If the couch is style 1, what is the probability that it will be made from fabric 2?

c). What is the probability that a couch of style 2 or style 4 will be selected at random?

d). If a couch is made from fabric 3, what is the probability that it is a style 3 couch?

e). What is the probability that a couch is made from fabric 3 and it is a style 3 couch?

f). What is the probability that a couch is not made from fabric 1?

Explanation / Answer

(a)

Out of 1000 couch, 460 made from fabric 1 so the probability that a couch picked at random will be made from fabric 1 is

P(fabric 1) =460 /1000 =0.460

(b)

Out of 305 style 1 couch, 55 are made from fabric 2 so the probability that it will be made from fabric 2 given that the couch is style 1 is

55 / 305 = 0.1803

(c)

Total number of counch of style 2 and style 4 is 215+255 = 470

So the required probability is 470 /1000 = 0.470

(d)

Out of 365 couches made up of fabric 3, 85 are of style 3 so requried probability is

85 / 365 = 0.2329

(e)

The requried probability is 85 /1000 =0.085

(f)

By the complement rule we have

P(not from fabric 1) =1 - P(fabric 1) =1 - 0.460 =0.540

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