We are interested in computing whether the event x is more or less probable than event evidence variable Y, i.e., whether P(X = x|Y) is greater than P(X x[Y). Given the = Bayes rule, what is the minimum number of distinct probabilities that x given an we need to have access to in order to answer this question and which ones?
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Q: Suppose E= "sum is 5" and F= "exactly one of the dice is even". Are E and F independent?
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- In the sport of basketball, a player will sometimes get the opportunity to shoot two free throws without being affected by any other players in the game. Assume that, for one player, these two free throws are independent of each other. If this player makes free throws 80% of the time, what is the probability that this player will make neither free throw in the opportunity?The probability of afternoon rain given morning cloud cover >50% is of interest to those forecasting the weather. You can calculate this probability using Bayes' Theorem (below). The probability of morning cloud cover in general is 30% in the area you are concerned with and when there's afternoon rain, morning cloud cover of the kind described above occurs 90% of the time. The probability of rain in general for the area is about 26% of days. From the above information, identify what P(BIA) would be. Express your answer as a proportion, rounded to two decimal places. P(A/B)= = P(B|A)*P(A) P(B)A nuclear reactor becomes unstable if both safety mechanisms A and B fail. The probabilities of failure are P(A) =1/300 and P(B) = 1/200. Also, if A has failed, B is then more likely to fail: P(B/A)=1/100. a) What is the probability of the reactor going unstable? b) If B has failed, what is the probability of the reactor going unstable?
- A researcher sets his decision criteria at p = .01. That is, she decides that she will reject the null hypothesis if the z – value she obtains has a probability of .01 or less. What is this researcher’s probability of making Type I error?Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table. Probabilities of Girls x(girls) P(x) x(girls)| P(x) |x(girls)| P(x) 0.000 0.122 10 0.061 1 0.001 0.183 11 0.022 2 0.006 7 0.210 12 0.006 3 0.022 8 0.183 13 0.001 4 0.061 9 0.122 14 0.000 Find the probability of selecting 12 or more girls. 0.001 O 0.022 0.006 O 0.007On a certain stretch of the East Coast Expressway, on average three birds per week are killed colliding with passing vehicles. The highway authority decides that if the probability of more than three birds per week being hit is more than 0.1, a special committee will be appointed to deal with the problem. Q1 (a) Determine whether the special committee will be appointed or not.
- Suppose that 20,000 married adults in a country were randomly surveyed as to the number of children they have. The results are compiled and are used as theoretical probabilities. Let X = the number of children married people have. P(x) ХP(x) 0.15 1 0.25 0.35 4 0.10 0.05 6 (or more) 0.05 (a) Find the probability that a married adult has three children. (Enter your answer to two decimal places.) (b) In words, what does the expected value in this example represent? O the average number of children married adults in the country have the average number of children adults in the country have O the number of children married adults in the country have O the number of children adults in the country have (c) Find the expected value. (Enter your answer to two decimal place.) children (d) Is it more likely that a married adult will have two to three children or four to six children? How do you know? O it is more likely to have two to three children, with p = 0.35 O it is more likely to have four…A company published the results of a study that found that arrogant workers are more likely to have poor performance ratings. Suppose that 15% of all full-time workers exhibit arrogant behaviors on the job and that 13% of all full-time workers will receive a poor performance rating. Also, assume that 10% of all full-time workers exhibit arrogant behaviors and receive a poor performance rating. Let A be the event that a full-time worker exhibits arrogant behavior on the job. Let B be the event that a full-time worker will receive a poor performance rating. Are events A and B independent? Why? Are the events A and B independent? Explain. A. No, because if workers exhibit arrogant behaviors, they are more likely to receive a poor performance rating. B. No, because if workers exhibit arrogant behaviors, they will receive a poor performance rating. C. Yes, because if workers exhibit arrogant behaviors, they are more likely to receive a poor performance rating. D. Yes, because if workers…Answers must be in 4 decimals |1. Ben plans to enforce speed limits using radar traps at 4 different locations within the campus. The radar traps at each of the locations L1, L2, L3, and L4 are operated 40%, 30%, 30%, and 20% of the time, and if a person who is speeding on his way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations, what is the probability that he will not receive a speeding ticket? 2. Barangay Scout Fernandez has one fire truck and one ambulance available for emergencies. The probability that the fire truck is available when needed is 0.95, and the probability that the ambulance is available when called is 0.90. in the event that there is a fire in the barangay, find the probability that both the ambulance and the fire truck will be available.
- Fatima has applied to study for her bachelor's at Zayed University and at UAE University. Let Z and U be the events of getting accepted at Zayed University and UAE University, respectively. The following table shows the marginal probabilities for events Z and U. U U₁ Complete the table if the events Z and U are independent. NN 2 Total No enough information NNĚ Z Z' Total U 0 0.3 0.3 Z Z' Total U 0.1 0.2 0.3 U 0.06 0.24 0.3 U' 0.2 0.5 0.7 U' 0.1 0.6 0.7 U' 0.14 0.56 0.7 Total 0.2 0.8 1 Total 0.2 0.8 1 Total 0.2 0.8 1 Z Z' Total 0.3 0.7 Total 0.2 0.8 1Show that the expectation of the sum of two random variables defined over the same sample space is the sum of the expectations. Hint: Let p1, p2, ··· , pn be the probabilities associated with the n sample points; let x1, x2, ··· , xn, and y1, y2, ··· , yn, be the values of the random variables x and y for the n sample points. Write out E(x), E(y), and E(x + y)A university computer laboratory installs one of three operating systems on each computer used in the lab. It is known from product testing that during an hour of web browsing the probability a computer with system 1 installed will crash is 0.15, the probability of a computer with operating system 2 crashing is 0.08 and the probability of a computer with system 3 crashing is 0.1. Operating systems 1 and 3 are installed on the same number of computers while system 2 is installed on twice as many computers as system 1 (or system 3).a) What is the probability that a randomly selected computer crashes during an hour of web browsing?b) If a computer selected at random crashed during an hour of browsing the web, what is the probability it has operating system 2 installed?c) If a computer selected at random does not crash during an hour of web browsing what is the probability it has operating system 1 or operating system 2 installed?
