A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement.Define the following events:- \( A : \{ \text{One of the balls is yellow} \} \)- \( B : \{ \text{At least one ball is red} \} \)- \( C : \{ \text{Both balls are green} \} \)- \( D : \{ \text{Both balls are of the same color} \} \)Find the following conditional probabilities:(a) \( P(\overline{A} \mid B) = \frac{1}{3} \)(b) \( P(D \mid \overline{B}) = \frac{1}{10} \)(c) \( P(D \mid \overline{C}) = \frac{1}{12} \)

We have given a box that contains one yellow, two red, and three green balls.We have to choose two…

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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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A person draws a card from a hat. Each card is one color, with the following probabilities of being drawn: 1/25 for pink, 1/10 for blue, 1/20 for red, and 1/15 for yellow. What is the probability of pulling a blue or red card, written as a reduced fraction?
A box contains 23 items, 7 of which are defective. If 5 are sold at random. Find the following probabilities : -Exactly 3 are not in good condition-None is defective and All are defective-At least 1 is defective.
The table summarizes the daily caffeine habits and majors of students at one university. Coffee Energy Drink No Caffeine STEM Major 0.32 0.13 0.02 Not STEM Major 0.17 0.27 0.09 Part A: Determine P(energy drink | STEM major) and describe the event in everyday language. Show all workPart B: Are the events consuming energy drinks and a STEM major approximately independent? Use probabilities to justify the answer.
A bag contains 3 red marbles and 4 white marbles. Two marbles are drawn in succession without replacement. What is the probabilities of the following events: The first marble drawn is red and the second is white: Both marbles drawn are red:
A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the following events: A : { One of the balls is yellow } B: { At least one ball is red } C:{ Both balls are green } D: { Both balls are of the same color } Find the following conditional probabilities: (a) P(A°|B) = (b) P(B|D) = (c) P(D|C°) =
A student takes a multiple-choice quiz with 5 questions, each with four possible answers and only oneof them is correct. A passing grade is 60% or better (i.e., answering at least 3 of 5 questions correctly).Suppose that the student was unable to find time to study for the exam and just guesses at eachquestion. Find the probabilities for the two events below.i. the student gets exactly 3 questions correct.ii. the student passes the exam
A group of students at a high school took a standardized test. The number of students who passed or failed the exam is broken down by gender in the following table. Determine whether gender and passing the test are independent by filling out the blanks in the sentence below, rounding all probabilities to the nearest thousandth. Male Female Passed P(male) = 28 14 Since P(male | pass) = so the events are Submit Answer Failed 18 9 and the two results are attemnt 1 of 2
Tina Fey goes trick-or-treating the night of Halloween dressed as Sarah Palin. She visits homes in her neighborhood to collect candy, but only receives candy, naturally, when the door is answered and the family still has a piece of candy to give away. Upon knocking, the probability of the door being answered is 3/4, and the probability that the home still has candy is 2/3. Assume that the events “Door answered” and “candy remaining” are independent and also that the outcomes at each home are independent. Also assume that each home gives away at most a single piece of candy. (c) Determine the probability that she receives her second piece of candy at the fifth house. (d) Given that she did not receive her second piece of candy at the second house(not sure if she receive her first candy), determine the conditional probability that she will receive her second piece of candy at the fifth house.

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