1.- A certain type of electric motor can only fail due to
obstruction of the bearings, combustion of the winding or wear of
the brushes. Suppose that the probability of obstruction is double
that of combustion; which is 4 times more likely than the wear of
the coils. What is the probability of failure due to wear of the
brushes?
Answer:
2.- Referring to the previous problem, determine the likelihood
that:
1) The intersection of paragraphs 2 and 4 of the previous
problem.
2) The union of paragraphs 3 and 4 of the previous problem
3) The intersection of paragraphs 3 and 5 of the previous
problem
4) The combination of paragraphs 1 and 2 of the previous
problem
5) The results are the same
**please answer both! thanks
1.
p(obstruction) = 2* p(combustion)
p(combustion) = 4* p(wear of coils)
Since p(obstruction) + p(combustion) + p(wear of coils) = 1
So 2* p(combustion) + p(combustion) + p(wear of coils) = 1
So 3 * p(combustion) + p(wear of coils) = 1
So 3 * 4* p(wear of coils) + p(wear of coils) = 1
So p(wear of brushes) = 1 / 13
Hence p(combustion) = 4* p(wear of coils) = 4* 1/13 = 4 / 13
Hence p(obstruction) = 2* p(combustion) = 2 * 4/13 = 8 / 13
2.
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