space. )' following Venn diagram shows the probabilities of various events in a sample 0.12 0.20 0.16 0.02 0.08 0.16 0.22 B What is the probability of the event whose region is marked ?
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- . A component is classified as one of top quality, standard quality or substandard quality. The probabilities of classified components are respectively 0.09, 0.81 and 0.10. Construct the Venn diagram of the classified events that helping you its linkage to mutual or non-mutual events. i. What is the probability that a component selected at random is either top quality or standard quality? ii. What is the probability that a component selected at random is not top quality? iii. What concept of the events did you give to different components?Q. 4 Let A, B, and C, be independent events with probabilities Par Pp, Pc of occurring, respectively. (i) What is the probability all 3 events occurring? (ii) What is the probability of none of them occurring? (iii) What is the probability that exactly 1 occurs?1 Rank the probabilities of 10%, 5, and 0.06 from the most likely to occur to the least likely to occur. O a Ob O c Od 1 0.06, 5, 10% 1 5, 10%, 0.06 1 10%, 5, 0.06 0.06, 10%, 5
- 2. You roll two six-sided dice. Fill in the table to find the product of the two dice. Then make a frequency table listingevery possible product, how often it occurs and then make a probability distribution bar graph. 3. Using the previous problem, find the sample space, S, of the product of the two dice. Let E be the event that theproduct is even. Let T be the event that the product is divisible by 3. Define the events E and T, then find the othersubsets:a) S = b) E =c) T = d) E^c =e) T^c = f) E U T = (are E and T mutually exclusive?) g)E^c ∩ T= h)E U T =1. Of the students in the college, 60% of the students reside in the hostel and 40% of the students are day scholars. Previous year result reports that 30% of all students who stay in the hostel scored A Grade and 20% of day scholars scored A grade. At the end of the year, one student is chosen at random and found that he/she has an A grade. What is the probability that the student is a hostlier? 2. Two players A and B are competing at a trivia quiz game involving a series of questions. On any individual question, the probabilities that A and B give the correct answer areαandβrespectively, for all questions, with outcomes for different questions being independent. The game finishes when a player wins by answering a question correctly. Compute the probability that A wins ifa. A answers the first question, b. B answers the first question. 3. Patients are recruited onto the two arms (0 - Control,1-Treatment) of a clinical trial. The probability that an adverse outcome occurs on the…A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below. Number of Breakdowns Probability 0 .12 1 .38 2 .25 3 .18 4 .07 The probability of at least 3 breakdowns in a month is _____. a. .30 b. .5 c. .10 d. None of these answers are correct.
- Q. 22 If A and B are independent events, how about the independence of their complements A and B?3.32 A pair of fair dice is tossed. Define the following events: A: B: {You will roll a 7.} (i.e., The sum of the dots on the up faces of the two dice is equal to 7.) {At least one of the two dice shows a 4.} a. Identify the sample points in the events A, B, An B, AUB, and Ac. b. Find P(A), P(B), P(A^ B), P(AUB), and P(A) by summing the probabilities of the appropriate sample points. c. Find P(AUB) using the additive rule. Compare your answer with that for the same event in part b. d. Are A and B mutually exclusive? Why?If ? and ? are two mutually exclusive events with ?(?)=0.2 and ?(?)=0.7, find the following probabilities: by the way, what's the c and d mean like Both A and B have A horizontal line over their heads
- g. Are the events “age of 30s” and “monthly spending of $250.00 or more” independent? Explain using probabilities.Refer to the Venn diagram to the right for events A and B in an equally likely sample space S. Find the indicated probability. P((ANB)') P((ANB)) = (Type a decimal.) 35 10 25 B 30K Suppose there is a 22.1% probability that a randomly selected person aged 30 years or older is a smoker. In addition, there is a 24.3% probability that a randomly selected person aged 30 years or older is male, given that he or she smokes. What is the probability that a randomly selected person aged 30 years or older is male and smokes? Would it be unusual to randomly select a person aged 30 years or older who is male and smokes? The probability that a randomly selected person aged 30 years or older is male and smokes is Would it be unusual? O Yes O No www (Round to three decimal places as needed.). wew
