d) If a strand is randomly selected, what is the probability that its conductivi

Question

d) If a strand is randomly selected, what is the probability that its conductivity is high?

e) What is the probability that the selected strand is either low in conductivity or high in strength?

f) If the selected strand has low strength, what is the probability that its conductivity is high?

Strands of copper wire from a manufacturer are analyzed for strength and conductivity. The results from 100 strands are as follows: Strength Low High 74 High conductivity Low conductivity 15 (a) If a strand is randomly selected, what is the probability that its conductivity is high and its strength is high? (b) If a strand is randomly selected, what is the probability that its conductivity is low or its strength is low? (c) Consider the event that a strand has low conductivity and the event that the strand has low strength. Are these two events mutually exclusive?

Explanation / Answer

a) probability that conductivity and strength is high =74/100=0.74

b)probability that  conductivity and strength is low =3/100=0.03

c)No as they have 3 strands in common they can not be mutually exclusive.

d)   probability that its conductivity is high =82/100=0.82

e)probability that the selected strand is either low in conductivity or high in strength =(18+74)/100=0.92

f)probability that conductivity is high given strength is low =8/11 =0.7273

strength high low total conductivity high 74 8 82 low 15 3 18 total 89 11 100

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