In a certain manufacturing process the probability of a type I defect is 0.21, the probability of a type II defect is 0.31, and the probability of having both types of defects is 0.01. Find the probability of having neither type of defect.

Hint:

Use P(A∪B)=P(A)+P(B)-P(A∩B)
and probability of having no defect is
1-P(A∪B).

To find the probability of having neither type of defect, we need to use the principle of complementary probabilities. The complementary probability of having a certain event is 1 minus the probability of that event occurring.

Let's denote the probability of having a type I defect as P(I), the probability of having a type II defect as P(II), and the probability of having both types of defects as P(I and II).

Based on the given information:
P(I) = 0.21 (probability of a type I defect)
P(II) = 0.31 (probability of a type II defect)
P(I and II) = 0.01 (probability of having both types of defects)

The probability of having neither type of defect can be calculated as follows:

P(neither) = 1 - (P(I) + P(II) - P(I and II))

Substituting the given values into the formula, we get:

P(neither) = 1 - (0.21 + 0.31 - 0.01)
= 1 - 0.51
= 0.49

Therefore, the probability of having neither type of defect is 0.49.