Problem 2An urn contains 5 white balls and 7 black balls. Draw aball and do not put it back into the urn. Then draw a second ball.(1) Define an appropriate probability space (2,A,P) to describe the experiment.(2) Describe the following events as subsets of the sample space :W₁ = "The first ball is white"B₁: "The first ball is black"W₂: "The second ball is white"B₂: "The second ball is black"(3) Compute P(W₂ | W1₁), P(W₂ | B₁), and P(W₂).(4) Are W₁ and W₂ independent? Justify your claim mathematically!

White balls 5 Black Balls 7 Note: As per the company guidelines first 3 questions will be…

Answered: Problem 2 ball and do not put it back…

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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5. A vegetable basket contains 12 peppers, of which 3 are red, 4 are green and 5 are yellow. Three peppers are taken, at random and without replacement, from the basket. c. The number of green peppers taken is denoted by the discrete random variable X. Draw up a probability distribution table for X.
400 randomly selected people are surveyed about income and education. Results are presented below: Low Income (L) Middle Income (M) High Income (H) College Degree (C) 32 73 120 No College Degree (N) 70 64 41 Based on this sample, find the probability that a randomly selected individual a. is high income, P(H)b. is a college graduate and is in the middle income bracket, P(C and M)c. is not a college graduate or is in the low income bracket, P(N or L)d. is in the high income bracket given that the individual has a college degree, P(H | C)e. has no college degree given the individual is in the middle income bracket, P(N | M)
One hundred college seniors attending a career fair at a univerisity were categorized according to gender and according to primary career motivation table below shows the results. If one of these students is to be selected at random, find the probability that the student selected will be a female. Money Allowed to be Sense of Total Creative Giving to Society Male 14 5 11 30 Female 2 35 33 70 Total 16 40 44 100 The probability of the student at the fair being female is _______. (Simplify your answer. Type an interger or a fraction.)
Consider the given event. Two indistinguishable dice are rolled; the numbers facing up add to 9. How many elements are in the sample space S? n(S) = = 30 List the elements of the given event E. (Select all that apply.) (1, 1), (2, 2), (3, 3), (4, 4), (5, 5) (2, 6), (3, 5), (4, 4) (3, 6), (4, 5) (1, 6), (2, 5), (3, 4) (1, 5), (2, 4), (3, 3) (1,4), (2, 3) Compute the probability of E. (Enter your probability as a fraction.) P(E) = 0.83 X
Let the sample space be S ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely. Compute the probability of the event E = "an odd number less than 8." P(E) = (Type an integer or a decimal. Do not round.)
A box contain 4 numbers: 1, 2, 4, 8 Two draws will be made, without replacement. Let the random variable X be the largest value drawn divided by the SQUARE of the smallest value drawn. Hint: if I were to draw the 8 and the 2, I take the largest draw (8) and divide by the square of the smallest draw (22 or 4) which yields 2. Hence, a possible value for X is 2. The following is the probability distribution of X Value of X ? 1 2 4 8 Probability 1/6 1/6 ? 1/6 1/6 What is the missing value of x? A) 0.25 B) 0 C) 0.5 D) 0.75 E) 16
First year university students were asked if they take any of the three courses listed in the Venn diagram. A student from this group is selected at random, what is the probability that this student takes both chemistry and Spanish? Chemistry Spanish 70 17 15 60 85 Math 5.7% 6.9% 9.2% 8.4%
All 400 employees at an accounting firm indicated what size of vehicle they drive: compact car, mid- size car, large car, or truck. The following table gives a two-way classification of their responses. Compact Car Mid-size Car Large Car Truck 54 48 Male Female 40 51 O b. 0.485, 0.2, 0.65, 0.5294. Management selects one employee at random. Let p₁ be the probability that the employee is a female, p2 the probability that the employee is a male and drives a mid-size car, p3 the probability that the employee is a female or drives a truck, and p4 the probability that the employee is a male knowing that the employee drives a truck. Then the P₁, P2, P3, and P4 are, respectively, (Choose one from the following which is closest to the correct answer.) O c.0.515, 0.2, 0.65, 0.5294. 80 73 O e. 0.515, 0.6675, 0.65, 0.5294. O d. 0.515, 0.2, 0.12, 0.5294. a. 0.515, 0.2, 0.65, 0.135. 20 34
Can someone help me out with these questions.
Suppose a sample of 100 people was taken, and each one was asked about being dominantly right-handed or left-handed. Their gender was also note. Handedness /Gender Right handed Left Handed Total Male 42 6 48 Female 45 7 52 Total 87 13 100 Suppose one person is chosen at random and compute the following probabilities. P(Female) P(Male or right-handed) P(Female given left-handed)

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