Statistics and Probability Assignment
2-26. Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized here:
Scratch
Resistance
Shock 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. Determine the number of disks in A B, A, and A B.
A B = 70, A= {9+5}= 14, A B ={70+16+9}= 95
2-86. Strands of copper wire from a manufacturer are analyzed for strength and conductivity. The results from 100 strands are as follows:
High conductivity
Low conductivity
Strength
High
Low
74
8
15
3
(a) If a strand is randomly selected, what is the probability that its conductivity is high and its strength is high?
P (High conductivity and high strength)= 74/100 =0.74
(b) If a strand is randomly selected, what is the probability that its conductivity is low or its strength is low?
P (Low strength or low conductivity) = P(Low conductivity) + P(Low strength) – P(Low conductivity and low strength) = (15+3)/100 + (8+3)/100 – 3/100 = 0.26
(c) Consider the event that a strand has low conductivity and the event that the strand has low strength. Are these two events mutually exclusive?
No, they are not mutually exclusive.
Because P(Low conductivity) + P(Low strength) = (15+3)/100 + (8+3)/100 = 0.29, which is not equal to P(Low conductivity and low strength).
2-106. A maintenance firm has gathered the following information regarding the failure mechanisms for air conditioning system:
Evidence of electrical failure
Evidence of gas leaks
Yes
No
Yes
55
17
No
32
3
The units without evidence of gas leaks or electrical failure showed other types of failure. If this is a representative sample of AC failure, find the probability
(a) That failure involves a gas leak
P (gas leak) = (55 + 32)/107 = 0.813
(b) That there is evidence of electrical failure given that there was a gas leak
P (electric
Scratch
Resistance
Shock 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. Determine the number of disks in A B, A, and A B.
A B = 70, A= {9+5}= 14, A B ={70+16+9}= 95
2-86. Strands of copper wire from a manufacturer are analyzed for strength and conductivity. The results from 100 strands are as follows:
High conductivity
Low conductivity
Strength
High
Low
74
8
15
3
(a) If a strand is randomly selected, what is the probability that its conductivity is high and its strength is high?
P (High conductivity and high strength)= 74/100 =0.74
(b) If a strand is randomly selected, what is the probability that its conductivity is low or its strength is low?
P (Low strength or low conductivity) = P(Low conductivity) + P(Low strength) – P(Low conductivity and low strength) = (15+3)/100 + (8+3)/100 – 3/100 = 0.26
(c) Consider the event that a strand has low conductivity and the event that the strand has low strength. Are these two events mutually exclusive?
No, they are not mutually exclusive.
Because P(Low conductivity) + P(Low strength) = (15+3)/100 + (8+3)/100 = 0.29, which is not equal to P(Low conductivity and low strength).
2-106. A maintenance firm has gathered the following information regarding the failure mechanisms for air conditioning system:
Evidence of electrical failure
Evidence of gas leaks
Yes
No
Yes
55
17
No
32
3
The units without evidence of gas leaks or electrical failure showed other types of failure. If this is a representative sample of AC failure, find the probability
(a) That failure involves a gas leak
P (gas leak) = (55 + 32)/107 = 0.813
(b) That there is evidence of electrical failure given that there was a gas leak
P (electric