Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 129 disks are summarized as follows:

shock Resistance

High Low

Scratch high 71 14

Resistance low 16 28

Let A denote the event that a disk has high shock resistance, and let B denote the event that a disk has high scratch resistance. If a disk is selected at random, determine the following probabilities. Round your answers to two decimal places (e. g. 98.77).

Find

1. P (A)

2. P (B)

3. P (A')

4. P (A ∩ B)

5. P (A U B)

6. P (A' U B)

The values are given as

P (A) = 0.67

P (B) = 0.66

P (A') = 0.33

P (A∩B) = 0.55

P (AUB) = 0.78

P (A'UB) = 0.88

Step-by-step explanation:

As from the given data

| Shock Resistance

| High | Low | Total

Scratch | High | 71 | 14 | 85

Resistance | Low | 16 | 28 | 44

Total | 87 | 42 | 129

As A=High Shock Resistance and B=High Scratch Resistance thus the values are calculated as

P (A) = 87/129=0.67

P (B) = 85/129=0.66

P (A') = 1-P (A) = 1-0.67=0.33

P (A∩B) = 71/129=0.55

P (AUB) = P (A) + P (B) - P (A∩B) = 0.67+0.66-0.55=0.78

P (A'UB) = P (A') + P (B) - P (A'∩B) = (42/129) + 0.66 - (14/129) = 0.88