Silicon wafers are used in the manufacture of integrated circuits. Of the wafers manufactured by a certain process, 10% have resistances below specification and 5% have resistances above specification.

a. What is the probability that the resistance of a randomly chosen wafer does not meet the specification?

b. If a randomly chosen wafer has a resistance that does not meet the specification, what is the probability that it is too low?

Solution :

Given the wafer manufactured by a certain process,it has 10% below resistances and

5 % above resistances.

Our goal is to find

a). What is the probability that the resistance of a randomly chosen wafer does not meet the specification?

b). What is the probability that it is too low?

Step 1 of 2 :

a).

Now we have to find the probability that the resistance of a randomly chosen wafer does not meet the specification.

Here let A and B be the event.

A denote the event that the resistance is above specification is 10%

10/100 = 0.1 and

B denote the event that the resistance is below specification is 5%

5/100 = 0.05

Then,

P(wafer does not meet the specification) =

Therefore the probability of resistance of a randomly chosen wafer does not meet the specification is 0.145