Question

Strands of copper wire from a manufacturer are analyzed for strength and conductivity. The results from 100 strands are as follows: High Strength Low Strength High conductivity 73 Low conductivity12 4 a) If a strand is randomly selected, what is the probability that its conductivity is high and its strength is high? Round your answer to two decimal places (e.g. 98.76) b) If a strand is randomly selected, what is the probability that its conductivity is low or the strength is low? Round your answer to two decimal places (e.g. 98.76) c) Consider the event that a strand has low conductivity and the event that the strand has a low strength. Are these two events mutually exclusive?

Answer 1

a)

P(High conductivity and High strength) = n(High conductivity and High strength) / Total stands

= 73 / 100

= 0.73

b)

P(low conductivity or low strength) = P(low conductivity) + P(Low strength) - P(low conductivity and low strength)

= 16/100 + 15/100 - 4/100

= 27/100

= 0.27

c)

Two events A and B are mutually exclusive if P(A and B) = 0

Since (P(low conductivity or low strength) = 4/100 = 0.4 $\neq$ 0,

The event that a strand has low conductivity and the event that the strand has a low strength are not

mutually exclusive.