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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)

Respuesta :

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Answer:

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

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