Exercise 2.2 (Probability of Joint Event) Test results of scratch resistance and shock resistance for 100 disks of poly carbonate plastic are as follows: Shock resistance Shock Resistance High (B) Low (B') Scratch High (A) 80 9 Resistance Low (A') 6 5 Let A and A’ denote the event that a disk has high scratch resistance and the event that a disk has low scratch resistance, respectively. Let B and B’ denote the event that a disk has high shock resistance and the event that a disk has low shock resistance, respectively. When a disk is selected at random, find the probability that both the scratch and shock resistances of the disk are high.
Exercise 2.2 (Probability of Joint
| Shock resistance | Shock Resistance | ||
| High (B) | Low (B') | ||
| Scratch | High (A) | 80 | 9 |
| Resistance | Low (A') | 6 | 5 |
Let A and A’ denote the event that a disk has high scratch resistance and the event that a disk has low scratch resistance, respectively. Let B and B’ denote the event that a disk has high shock resistance and the event that a disk has low shock resistance, respectively.
- When a disk is selected at random, find the probability that both the scratch and shock resistances of the disk are high.
- When a disk is selected at random, find the probability that the scratch or shock resistance of the disk is high.
- Consider the event that a disk has high scratch resistance and the event that a disk has high shock resistance. Are these two events mutually exclusive?
Exercise 2.3 (Conditional Probability) In exercise 2.2, find the probability that a disk has high scratch resistance (A) when it has high shock resistance (B)
Exercise 2.5 ( Independence) For the resistance test results in Exercise 2.2, the following probabilities have been calculated:
P(A) and P(A | B) =
Asses if events A and B are independent.
*Answer all the exercises with complete solutions.
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