3. In order to combat smuggling, the customs will inspect any three incoming vessels.Let A={the ith ship sampled is a smuggling ship},i=1, 2, 3Use A₁, A2 and 43 to represent the following events:(4) None of the three ships is a smuggler;(5) All three ships are smugglers ;(6) There are at most two smugglers.

Answered: 3. In order to combat smuggling, the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose that we have a data set of doctoral students in economics. This data set includes whether each student had a major in economics from his or her undergraduate institution and whether the same student earned a master's degree before starting a PhD program. Also, this data set includes information on which subfield of economics the student is interested in. Let's define the events E, M, FMicro, FMacro, and FMetrics as follows: E = {Economics major} M = {Having a master degree} FMicro = {Choosing microeconomics as a sub-field} FMacro = {Choosing macroeconomics as a sub-field} FMetrics = {Choosing econometrics as a sub-field} FMicro FMacro FMetrics Total E∩M .150 .150 .100 .400 E∩MC .050 .075 .050 .175 EC∩M .050 .100 .050 .200 EC∩MC .050 .150 .025 .225 Total .300 .475 .225 1) Suppose we learn that a student got a major in economics. What probability should we assing to the event that this student does NOT have a master's degree? 2) Suppose we learn that a…
8. Let A, B be two events with P(A) = ½, P(A − B) = 3, determine P(AB).
The highways connecting two resorts at A and B are sometimes closed due to snow and ice. Let E,, E, and E, denote the events that highways AB and AC and CB are passable, respectively. From past years' records: 3 P(E,) =. P(E,) =, P(E,) =, =. 4 P(E,\ E,) = and P[E, |(E,nE,)]= 4 What is the probability that a traveler will be able to get from A to B? E, E2 Hint: Define E: the event that a traveler can get from A to B E= E, U(E,E), and %3D compute P(E) to find the probability that a traveler will be able to get from A to B, ie. P(E), for this computation use the definition of conditional probability and compute P(E) to find the probability that a traveler will be able to get from A to B, i.e. P(E), for this computation use the definition of conditional probability.
Of the 30 college students who visited the campus health center yesterday, 9 received prescriptions while the remaining 21 did not. The following table further categorizes these 30 students by gender: Male Female Prescription P 6 3 No Prescription N 12 9 1- Using these data, estimate P(N) and P(F). 2- Estimate P(N and F). 3- Based on (1), what would the answer to (2) have been if the events N and F were independent? Are N and F independent? Explain
1. Suppose U and V are mutually exclusive events with P(U) = 0.45; P(V) = 0.37. Find: P(U and V) = P(U|V) = P(U or V) =
4. A newspaper story claims that more houses are purchased by singles now than singles 5 years ago. To test this claim, two studies were conducted on the buying habits of singles over the past 5 years. In the first study, 200 house purchases in the current year were randomly selected and 80 of those were made by singles. In the second study, again 200 house purchases were randomly selected from 5 years ago and 57 of those were made by single people. Test the newspaper's claim using a 0.05 level of significance. Is there sufficient evidence to support the newspaper's claim? Let singles now be Population 1 and let singles 5 years ago be Population 2. Step 1. State the null and alternative hypotheses for the test. Fill in the blank below. A) Step 2. Compute the value of the test statistic. Round your answer to two decimal places. Step 3. Draw a conclusion and interpret the decision. A) We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level…
16. Given that two events A and B are mutually exclusive, P(An B) is: a. b. C. d. 17. At a pet store you can choose between 6 fish species, 2 mini frog species, and 4 plant species. You want your tank to contain one fish, one frog, and one plant. How many different setups are possible for your tank? a. 12 b. 48 C. 3 d. 0 0.50 1 None of these a. b. 18. A set of data is normally distributed with a mean of 7 and a standard deviation of 2.5. Calculate the z- score for the data value x = 5: C. d. 122 0.80 -0.80 0.90 -0.90
1) Given two events A and B: P(A) = .3, p(B) = .5, P(A|B) = .7 Then a) P(A n B) = b) P(B|A)=
1. Events A and B are mutually exclusive with P(A) = 0.280 and P(A or B) = 0.740 a) P(B)= b) P(Not A)= c) P(A and B)=
6. Let A, B, C be three events with P(A) = P(B) = P(C) = 1, P(AC) = 1, P(AB) = P(BC) = 0, determine the probability of the event that at least one of A, B, C occurs.
5. A group of n people stand in a line. On the count of three, each of them simultaneously chooses to look either left or right (with equal probability): at one of their neighbors. Let X be the number of pairs of adjacent people that end up facing each other. (For example, if n = 5 and the random facings are "Left, Left, Right, Left, Right" then only the 3rd and 4th people face each other.) (a) Find the expected value E[X]. (b) Find Pr[X=0]. (c) Assuming n is even, find the maximum possible value of X, and the probability that X is equal to that value.

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