Answer:
Part a
The probability that the event disk has high shock resistance is 0.86
Part b
The probability that a disk has high scratch resistance given that the disk has high shock resistance is 0.8140
Step-by-step explanation:
(a).
From the given information,
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.
SHOCK HIGH(A) SHOCK LOW(A) TOTAL
SCRATCH
HIGH(B) 70 9 79
RESISTANCE 16 5 21
LOW(B)
TOTAL 86 14 100
Compute P(A).
Therefore, the probability value of the event A is 0.86.
Part a
The probability that the event disk has high shock resistance is 0.86
Explanation | Hint for next step
Based on the given information, the probability that the event disk has high shock resistance is 0.86. That means it is approximately equal to 86%.
Step 2 of 2
(b)
From the given information,
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.
SHOCK HIGH(A) SHOCK LOW(A) TOTAL
SCRATCH
HIGH(B) 70 9 79
SCRATCH
LOW(B) 16 5 21
TOTAL 86 15 100
ComputeP(B/A) = P(A∩B) /P(A) ;P(A) > 0
P(A∩B) =70/100
=0.70
From the part [a], the probability value of the event A is P(A) =0.86 .
Therefore,
P( {B/A} = P(A∩B) /P(A)
= 0.70 /0.86
=0.8140
Part b
The probability that a disk has high scratch resistance given that the disk has high shock resistance is 0.8140
Explanation | Common mistakes
The disk with high scratch resistance is found to be 81.40% with the condition that the disk with high shock resistance is maintained.
