Strands of copper wire from a manufacture are analyzed for strength and conducti

Question

Strands of copper wire from a manufacture are analyzed for strength and conductivity. The results from 100 strands are as follows: If a strand is randomly selected, what is the probability that its conductivity is high and its strength is high? If a strand is randomly selected, what is the probability that its conductivity is low or the strength is low? Consider the event that a strand has low conductivity and the event that the strand has low strength. Are these two events mutually exclusive? In a shipment of 52 parts, there are 4 defective parts. A random sample of 5 parts is drawn without replacement from this shipment. Let X be the number of defective parts the random sample. Find the probability mass function, f(x), of X. Find P(X lessthanorequalto 1).

Explanation / Answer

(a) P(High and High) = 74/100 = 0.74

(b) P(Low or Low) = P(Conductivity is low) + P(Strength is low) - P(Both are low)

= 18/100 + 11/100 - 3/100 = 26/100 = 0.26

(c) The events low conductivity and low strength are not mutually exclusive since there are 3 dtrands which have low conductivity and low strength.

Strength High Low Total High 74 8 82 Conductivity Low 15 3 18 Total 89 11 100

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