MATH 201 Introduction To Probability & Statistics Homework 4 Dr. Hany Nasr Hassan Q1: Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows: 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 following probabilities: Q2: The probability that an automobile being lled with gasoline also needs an oil change is 0.25; the probability that it needs a new oil lter is 0.40; and the probability that both the oil and the lter need changing is 0.14. (a) If the oil has to be changed, what is the probability that a new oil lter is needed? (b) If a new oil lter is needed, what is the probability that the oil has to be changed? Q3: A student is taking two courses A and B. He estimates his probability of failing in the first course at 0.32 and in the second course at 0.25 and if failing in the two courses A and B are independent from each other, find the: (a) Probability that he will fail in both classes (b) Probability that he will fail in A or B (c) Probability that he will fail in A if he already failed the B (d) Probability that he will pass in B if he already failed the A (e) Probability the he will pass both courses Q4: A lot of 50 spacing washers contains 30 washers that are thicker than the target dimension. Suppose that three washers are selected at random, without replacement, from the lot. (a) What is the probability that all three washers are thicker than the target? (b) What is the probability that the third washer selected is thicker than the target if the first two washers selected are thinner than the target? (c) What is the probability that the third washer selected is thicker than the target? MATH 201 Introduction To Probability & Statistics Homework 4 Dr. Hany Nasr Hassan Q5: Suppose A and B are mutually exclusive events. Construct a Venn diagram that contains the three events A, B, and C such that (/) = 1 and (/) = 0