Question 24.2: Five bolts with internal cracks are accidentally mixed with ...

Given Number of bolts without defect = 95
Number of bolts with defect = 5
Step I Probability of using defective bolts
In this example, the event (E) is to use a defective bolt. Out of 100 bolts, five are defective. Therefore, the event can happen in five (f = 5) ways out of one hundred (n = 100) equally likely ways.

p=P(E)=\frac{f}{n}=\frac{5}{100}=0.05 .

Step II Probability of not using defective bolts
The probability of not event (\tilde{E}) , namely, not using the defective bolt, is given by,

q=P(\tilde{E})=1-p=1-0.05=0.95 .

Also, p + q = 0.05 + 0.95 = 1
The physical significance of the number 1 is that there is a certainty of using either a defective or non-defective bolt in the assembly shop.