The following probability exercises relate to circuit components that are tested

Question

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 outisde of the tolerance specifications?

Explanation / Answer

Ans:1)0.5*0.5*0.5=0.125

2)0.5^3+0.2^3+0.3^3=0.125+0.008+0.027=0.16

3)0.5*0.94+0.2*0.96+0.3*98=probability of a part being in specification=0.956

Probability of being a part not to specification=1-0.956=0.044

4)0.5*0.06=0.03

5)0.044*n=10

n=227.27

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