Week 10 Exercise Probability The following probability exercises relate to circu

Question

Week 10 Exercise

Probability The following probability exercises relate to circuit components that are tested in a production line to check whether they're within tolerence specifications. 50% of componenents produced are resistors which have a 94% chance of being within tolerance specifications, 20% of components are inductors which have a 96% chance of being made to specification and the remaining components are capacitors which have a 98% chance of being made to specification. Please answer the following questions:
1. What is the probability that the first three circuit elements on the production line are resistors?
2. What is the probabability that the first three circuit elements on the production line are all the same type of element?
3. What is the probability that a random circuit elements on the production line is within the tolerance specifications?
4. If a circuit element was found to not meet tolerance specifications, what is the probability that the element is a resistor?
5. On average, how many circuit elements would go along the production line until 10 elements were found to be outside of the tolerance specifications?

Explanation / Answer

1)

the probability that the first three circuit elements on the production line are resistors = 0.5*0.5*0.5 = 0.125

2)

the probabability that the first three circuit elements on the production line are all the same type of element

= 0.5^3 + 0.2^3 + 0.3^3 = 0.125+0.08+0.027 = 0.160

3)

the probability that a random circuit elements on the production line is within the tolerance specifications =

P(Resistors within specs) + P(Inductors within specs)+P(capacitors within specs)

0.5*0.94 + 0.2*0.96+0.3*096 = 0.956

4)

P(NElement is resistor| not within the specs) = P(not within the specs and element is resistor) / P(Resistor) = 0.5* 0.06 / (1-0.956) = 0.682

5)

P(Circuits not within the specs) = 1- 0.956 = 0.044

So for every 1000, 44 will be out of the specs limits.

for 10 , total no should be 10/0.044 = 228

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