Question

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

Answer 1

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.

Question is incomplete