Suppose a firm makes couches in four different styles and three different fabric
ID: 3124846 • Letter: S
Question
Suppose a firm makes couches in four different styles and three different fabrics. Use the table to calculate the probability that a couch picked at random will be made from fabric 1. If the couch is style 1, what is the probability that it will be made from fabric 2? What is the probability that a couch of style 4 will be selected at random? If a couch is made from fabric 3, what is the probability that it is a style 3 couch?
Fabric
Style
F1
F2
F3
Total
S1
150
55
100
305
S2
120
25
70
215
S3
80
60
85
225
S4
110
35
110
255
Total
460
175
365
1000
Fabric
Style
F1
F2
F3
Total
S1
150
55
100
305
S2
120
25
70
215
S3
80
60
85
225
S4
110
35
110
255
Total
460
175
365
1000
Explanation / Answer
Use the table to calculate the probability that a couch picked at random will be made from fabric 1.
P(F1) = 460/1000 = 0.46 [ANSWER]
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If the couch is style 1, what is the probability that it will be made from fabric 2?
P(F2|S1) = 55/305 = 0.180327869 [ANSWER]
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What is the probability that a couch of style 4 will be selected at random?
P(S4) = 255/1000 = 0.255 [ANSWER]
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If a couch is made from fabric 3, what is the probability that it is a style 3 couch?
P(S3|F3) = 85/365 = 0.232876712 [ANSWER]
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