Suppose we have a trlangle made of the 3 vertices A, B, and C, and the 3 edges AB, BC, AC. We color each vertex blue or red uniformly at random. Then define 3 random variables(one for each edge) that Indicate whether the edge's vertices are the same color. Are these three random varlables mutually independent?

Answered: Suppose we have a triangle made of 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 you are making a six faces dice. With each of the six faces, you need to put a number 1 to 6 on the faces so that each number is on a distant face. How many different dice can you make? (two dices are considered different if it is impossible to rotate the cube to match one another)
A box contains r red balls and b blue balls. One ball is selected at random and its color is observed. The ball is then returned to the box and k additional balls of the same color are also put in the box. A second ball is then selected at random, Its color is observed & it's returned to the box together with k additional balls of the same color. Each time another ball is selected, the process is repeated. If four balls are selected, whats the probability that the first three balls will be red and the fourth be blue?
Consider a deck of 52 cards with 4 suits and 13 cards (2-10,J,K,Q,A) in each suit. Jack takes one such deck and arranges them in a line in a completely random order. Now he wants to find the number of "Power Trios" in this line of cards. A "Power Trio" is a set of 3 consecutive cards where all cards are either a Jack, Queen or King (J,Q or K). A "Perfect Power Trio" is a set of 3 consecutive cards with exactly 1 Jack, 1 Queen and 1 King (in any order). Find the expected number of Power Trios that Jack will find. Find the expected number of Perfect Power Trios that Jack will find.
At a tourist place, it has been observed that: 40% of the women like to travel with a Purse, 30% of the women like to travel with a Sunglass, 35% of the women like to travel with a Watch, and it is also noted that: 12% of the women like to travel with a Purse and a Sunglass, 3% of the women like to travel with all these three luxuries, 10% of the women like to travel with a Purse and a Watch, and 8% of the women like to travel only with a Sunglass. Purse Watch Sunglass Modern women like luxury. A woman What percentages of the women like to travel with Watch only? a. 30% b. 27% ♥ What percentages of the women do not like to carry them C. 40% (Purse, Sunglass, Watch)? v What percentages of women like to travel with Purse only? v What percentages of women like to travel with both Watch f. 13% and Sunglass? d. 65% e. 15% g. 52% v What percentages of women like to travel either with Watch or with Sunglass? v What percentages of women like to travel with Sunglass only? h. 8% i. 21%
2.3 4) Consider each situation. Decide whether the pairs of events are mutually exclusive or not. a) Roll a die: Get an even number and get a number less than 3. b) Roll a die: Get a prime number (2, 3, or 5) and get a six. c) Roll a die: Get a number greater than 3 and get a number less than 3. d) Select a student: Get a student with blue eyes and get a student with blond hair. e) Select a college student: Get a sophomore and get a student that is a math major. f) Select a course: Get an Algebra course and get an English course. g) Select a voter: Get a Republican and get a Democrat. INTL DII %23 3. 4 5 6. e y
The geographical distribution of the hometown of 80 students of PUP is given as: 50 from Luzon, 10 from Visayas, and 20 from Mindanao. (1) How many ways can three students be selected at random such that NO student comes from Luzon and Mindanao.(2) How many ways can three students be selected at random such that all of them come from any of the three places.
Bowl A contains 2 red chips; bowl B contains two white chips; and bowl C contains 1 red chip and 1 white chip. A bowl is selected at random, and one chip is taken at random from that bowl.
Read the paper above and answer question # 4 only

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