Strands of copper wire from a manufacturer are analyzed for

Strands of copper wire from a manufacturer are analyzed for strength and conductivity.The results from 100 strands are as follows:

a) If a strand is randomly chosen, what is the probability that its conductivity is highand strength is high?

b) If a strand is randomly chosen, what is the probability that its conductivity is low orstrength is low?

c) For a) and b), did you use classic approach or empirical approach to calculate theprobabilities?

d) Consider the event that a strand has low conductivity and the event that the strandhas low strength. Are these two events mutually exclusive?

e)  Are two events in d) independent? (Answer this question using the theoreticaldefinition)

Solution

Strands of copper wire from a manufacturer are analyzed for strength and conductivity.The results from 100 strands are as follows:

High Stength

Low Strength

High Conductivity

74

8

82

Low Conductivity

15

3

18

89

11

100

a) If a strand is randomly chosen, what is the probability that its conductivity is highand strength is high?

P=74/100=0.74

b) If a strand is randomly chosen, what is the probability that its conductivity is low or strength is low?

P=(18+11-3)/100 =26/100=0.26

c) For a) and b), did you use classic approach or empirical approach to calculate theprobabilities?

We use classic approach.

d) Consider the event that a strand has low conductivity and the event that the strand has low strength. Are these two events mutually exclusive?

No, two events are not mutually exclusive because 3 strand are common to both events.

e)  Are two events in d) independent? (Answer this question using the theoretical definition)

No, the events are not independent.

P(Low Conductivity ) =18/100=0.18

P(Low Conductivity/ Low Strength ) =3/11 =0.2727

P(Low Conductivity ) P(Low Conductivity/ Low Strength )