Disks of polycarbonate plastic from a supplier are analyzed for scratch and shoc
ID: 3048379 • Letter: D
Question
Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 120 disks are summarized below: shock resistance 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. low scratch resistancew high low 19 10 21 1. Determine the number of disks in: AandB notA AorB AorB' 2. Are the events A, B mutually exclusive? Why? 3. If a disk is selected at random, determine the following probabilities: P(A)- P(B)- P(AandB)- P(AorB)-P(A) + P(B)-P(AandB)- 4. If a disk is selected at random, what is the probability that its scratch resistance is low and its shock resistance is high?Explanation / Answer
Answer) Given,
A total of 120 disks are analysed
Shock Resistance
Scratch Resistance
High
Low
High
70
19
Low
21
10
Event A indicates disk has high shock resistance
Event B indicates disk has high scratch resistance
1a) (A Ç B)=70
1b)(A)=(19+10)=29
1c)(AB)=(70+21+19)
(AÈB)=110
1d) (AB)=(70+21+21+10-21)
(AÈB)=101
2) For mutually exclusive events, P(A B) should be equal to zero
Events A and B are not mutually exclusive events as P(A B)=0.58 and not equal to zero
3a) P(A)=(70+21)/120=91/120
P(A)=0.76 or 76%
3b) P(B)=(70+19)/120
P(B)=74.16% or 0.74
3c)P(A B)=70/120
P(A Ç B)=0.58 or 58%
3d) P(AB)=110/120
P(AÈB)=0.92 or 92%
4) we need to find P(AB
P(AB
P(AÇB)=0.175 or 17.5%
Shock Resistance
Scratch Resistance
High
Low
High
70
19
Low
21
10