Question

Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows:

shock resistance
scratch resistance high low
high 70 9
low 16 5

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. Input your answers in the fractional form (do not simplify).

P(A)=86/100

P(B)=79/100

P(A')=7/50

P(A U B)=95/100

P(A' U B)= ???

Answer 1

0.84

Explanation:

Given that Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows:

P(A) = 0.86, P(B) = 0.79, P(A') = 0.14, P(AUB) = 0.95

We are to find out P(A'UB)

We have

`P(AUB) =P(A)+P(B)-P(A\bigcap B)\\0.95=0.86+0.79-P(A\bigcap B)\\P(A\bigcap B)=0.70`

`P(A'UB) = P(A')+P(B)-P(A' \bigcap B)\\= 1-P(A) +P(B)-[P(B)-P(A \bigcap B)]\\= 1-0.86+0.79-P(B)+[tex]P(A'UB)=0.14+0.79-0.79+0.70\\=0.84`P(A \bigcap B)[/tex]