involving events E, F, and G in a sample space S. Assume that Pr[E]=0.65, Pr[F]=0.45, Pr[G]=0.5, Pr[E∩F]=0.3, Pr[E∩G]=0.35, and Pr[F∩G]=0.3. Find the following probabilities: (1) Pr[E∪F]= (2) Pr[F′∩G]= (3) Pr[E′∩G′]=

involving events E, F, and G in a sample space S. Assume that Pr[E]=0.65, Pr[F]=0.45, Pr[G]=0.5, Pr[E∩F]=0.3, Pr[E∩G]=0.35, and Pr[F∩G]=0.3. Find the following probabilities: (1) Pr[E∪F]= (2) Pr[F′∩G]= (3) Pr[E′∩G′]=

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...

See similar textbooks

Similar questions

Let E and F be events in a sample space S with probabilities p (E)= and p (F) = such that the conditional probability of F given E is p(FE) = Determine p(EF). 0 / / 75 O None of these.
Assume that 12 jurors are randomly selected from a population in which 80% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities. xx P(x)P(x) 0 0+ 1 0+ 2 0+ 3 0.0001 4 0.0005 5 0.0033 6 0.0155 7 0.0532 8 0.1329 9 0.2362 10 0.2835 11 0.2062 12 0.0687 Find the probability of exactly 7 Mexican-Americans among 12 jurors. Round your answer to four decimal places.P(x=7)=P(x=7)= Find the probability of 7 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places.P(x≤7)=P(x≤7)= Does 7 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans? no yes
A branch of a certain bank has six ATMs. Let X represent the number of machines in use at a particular time of day. The cdf of X is as follows: F(x) = (b) Calculate the following probabilities directly from the cdf: (a) p(2), that is, P(X = 2) (c) 0 0.09 0.21 0.33 0.53 0.90 0.99 1 P(X > 3) x < 0 0 < x < 1 1 ≤ x < 2 2
Q P.6: On its way, a car meets 4 traffic lights, and the probability that each of them will be red is 0.5. Let X be a discrete random variable equal to the number of traffic lights that were green when the car arrived. X may take the values of 0, 1, 2, 3, 4. (Assume traffic lights are independent.) What is the probability distribution of X? The probability distribution of X is 3 4 p(x) 0.5 0.25 0.125 0.0625 0.0625 The probability of distribution of X is 3 p(x) 0.5 0.5 0.25 0.125 The probability of distribution of X is 3 4 p(x) 0.5 0.25 0.5 0.25 0.125 The probability distribution of X is 1 3 4 p(x) | 0.5 || 0.5 || 0.5 | 0.5 || 0.5 The probability of distribution of X is 3 4 p(x) || 0.0625 0.0625 0.125 0.25 0.5
0.10.20.40.5
I need help with this:A manufacturer knows that on average 20% of toasters produced require repairs within 1 year after they are sold. When 18 toasters are randomly selected, find the smallest number x and largest number y such that (a) the probability that at least x of them will require repairs is less than 0.58; (b) the probability that at least y of them will not require repairs is greater than 0.84.
Consider the sample space {a,b,c,d,e} with probabilities, respectively, .1,.2,.3,.2,.2. Verify that this is a probability space. The random variable X is given by X(a)=1, X(b)=2, X(c)=3. X(d)=4 and X(e)=5. Compute the expected value and variance of X. Let X2 be two iterations of X, addeed, independently. Write down an appropriate probability space for this and compute the expected value and variance of X2 two different ways- directly from the probability space, and also by using our theorems, (If you think of X as the outcome of some game, then X2 is the result of playing the game twice, independently.)
Assume that 12 jurors are randomly selected from a population in which 83% of the people are Asian-Americans. Refer to the probability distribution table below and find the indicated probabilities. xx P(x)P(x) 0 0+ 1 0+ 2 0+ 3 0+ 4 0.0002 5 0.0013 6 0.0073 7 0.0305 8 0.0931 9 0.2021 10 0.296 11 0.2627 12 0.1069 Find the probability of exactly 7 Asian-Americans among 12 jurors.P(x=7)=P(x=7)= Find the probability of 7 or fewer Asian-Americans among 12 jurors.P(x≤7)=P(x≤7)=
Q. 1 Deal two cards from a well-shuffled deck of cards. Let the random variable X be the number of aces dealt and let the random variable Y be the number of face cards dealt. (i) Find and sketch fx.y (x, y).
Assume that 12 jurors are randomly selected from a population in which 71% of the people are Asian-Americans. Refer to the probability distribution table below and find the indicated probabilities. x� P(x)�(�) 0 0+ 1 0+ 2 0.0001 3 0.0011 4 0.0063 5 0.0246 6 0.0704 7 0.1477 8 0.2261 9 0.246 10 0.1807 11 0.0804 12 0.0164 Find the probability of exactly 8 Asian-Americans among 12 jurors.
A sample space has 3 outcomes, {O1, O2, O3}. Suppose E= {O1, O2}, and F= {O1, O3}. If Pr[E]= 0.67 and Pr[F]= 0.54, what is Pr[{O2, O3}]?