4) You are performing quality control for a nuclear test loop; specifically, you

Question

4) You are performing quality control for a nuclear test loop; specifically, you are investigating failure modes for valves. You gather the following information regarding valve failures: Evidence of Gas Leaks Yes No 17 Evidence of electrical failure Yes No 32 Assuming that this sample is representative of the population of valves, find the following: (5 points) The probability a failure involves a gas leak: a. b. (5 points) The probability of evidence of a gas failure given that there is evidence of an electrical failure: (5 points) The probability of evidence of an electrical failure given that there is no evidence of a gas failure: c. (5 points) Consider the probability of gas failure evidence and the probability of electrical failure evidence. Are these two probabilities independent? Explain your reasoning (preferably mathematically but in words is fine too I guess) d.

Explanation / Answer

4. Write back to me in case of doubts.

a. P(failure involves a gas leak) = Yes, for evidence of gas leak/total

= (55+32)/(55+32+17+3)

=.8131

b. P(chances of gas leak, given evidence of electrical failure)

= Yes, for eveidence of gas leaks and elec failure/Yes, for for evidence of
electrical failure

= 55/(55+32)

= .6322

c. P(evidence of elec failure given that no evidence of gas failure)

= total with evidence of elec failure and no evidence of gas leaks/total with no to gas leaks

= 17/17+3

= .85

d.P(evid of elec failure) = (55+17)/(55+17+32+3) = .6729
P(evid of gas leaks) = (17+3)/(55+17+32+3) = .1869
P(evid of elec failure and gas leak) = 55/(55+17+32+3) = .5140

A and B events aer independent if P(A and B) = P(A)*P(B)
Here, .6729*.1869 != .5140, so , they aren't independent

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