Question

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')

Answer 1

Answer: 1) 0.674, 2) 0.659, 3) 0.326.

Step-by-step explanation:

Since we have given that

Shock Resistance            High          Low      Total

Scratch high                       71               14           85

Resistance low                   16               28          44

Total                                   87              42           129

A be the event that a disk has high shock resistance

B be the event that a disk has high scratch resistance

1) P(A) is given by

$\dfrac{87}{129}=0.674$

2)  P(B) is given by

$\dfrac{85}{129}=0.659$

3) P(A') is given by

$P(A')=1-P(A)\\\\P(A')=1-0.674\\\\P(A')=0.326$

Hence, 1) 0.674, 2) 0.659, 3) 0.326.