Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows: Shock Resistance High Low High 70 Scratch Resistance Low 16 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. Events A and Bare independent. O No. Yes.
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- 1. Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized below: Shock resistance High 70 16 Low Scratch resistance High Low 9. 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. A' b. В C. ANB d. AuB 2. The rise time of a reactor is measured in minutes (and fractions of minutes). Let the sample space for the rise time of each batch be positive, real numbers. Consider the rise times of two batches. Let A denote the event that the rise time of batch 1 is less than 72.5 minutes, and let B denote the event that the rise time of batch 2 is greater than 52.5 minutes. Describe the sample space for the rise time of two batches graphically and show each of the following events on a two-dimensional plot: а. А b. B' C. ANB d. AUB 3. Samples of emissions from three suppliers are classified for…We flip a fair coin two times. Remember that for a fair coin, the probability of landing on heads (H) is 1/2 and the probability of landing on tails (T) is also 1/2. The flips are independent. If the outcomes from both flips are the same (HH or TT) we win, otherwise we lose. Define the following events: A: heads for the first coin flip. • B: heads for the second coin flip. C: we win. What is the probability that all three events happen, P(AN Bn C)? 1/2 1/3 1/4Suppose we roll two six-sided dice. Consider event A as getting an odd number on die 1, event B asgetting an even sum for the two dice. Are event A and B independent?
- A study of the incoming freshman class at a university found that 60% of the students had taken AP Calculus in high school, 55% had taken AP English in high school, and 20% had taken both AP Calculus and AP English. One incoming freshman is randomly selected from the population of incoming freshman. Let: C = the selected student took AP Calculus E = the selected student took AP English What is the probability that the selected incoming freshman took AP English or AP Calculus, i.e. P( C or E)? 0.15 O 0.75 0.80 0.05 0.95Let V be the event that a randomly chosen person takes a daily multivitamin. Let C be the event that a randomly chosen person has had a cold this year. Place the correct event in each response box below to show: Given that the person takes a daily multivitamin, the probability that a randomly chosen person has had a cold this year. Provide your answer below: P( | )Refer to the hospital emergency department data. Hospital 1 2 3 4 Total Total 5292 6991 5640 4329 22,252 LWBS 195 270 246 242 953 Admitted 1277 1558 666 984 4485 Not admitted 3820 5163 4728 3103 16,814 Let A denote the event that a visit is to hospital 1, and let B denote the event that a visit results in admittance to any hospital. Determine the number of persons in each of the following events. AnB and A U B'. (Show complete solutions in your answer sheet) O a. None among the choices O b. 13752, 19044 Oc. 1277, 6915 O d. 1277, 19044
- Suppose that a fair, 6 sided die is rolled. Let X indicate the event that an odd number is rolled (in other words, X = 1 if an odd number is rolled and X = 0 otherwise). Let Y indicate the event that 2, 3, or 4 is rolled (in other words, Y = 1 if 2, 3, or 4 is rolled and Y = 0 otherwise). Find P (X = 0, Y = 1). b) O% c) d) e) O½ A O None of the aboveO A. 0 OB. 0.5 O C. 1 OD. A z-table is needed. 7. Define the following events: X = event that an athlete takes vitamin X Y = event that an athlete takes vitamin Y Z = even that an athlete takes vitamin Z Which of the following is equivalent to the event that an athlete chosen random does not take any of the 3 vitamins? 0000 A. AUBUC B. (AUBUC) OC. AUBUC OD. None of the above 8. If A is any event in Q, what is P(A U Q)? *only g,h,i
- Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.What is the probability that the student was female and got a BSuppose that in a group of 28 people, there are 5 who test positive for a virus. You take a random sample of two people from this group. a. The events "First person chosen has thelvirus" and "Second person chosen has the virus" are: O dependent O independent Find the probability (round to three decimals) that: b. Both people have the virus. C. Neither person has the virus. d. At least one of the two people has the virus. e. The first person chosen has the virus and the second does not. Submit Question