5. An art competition has 30 entries from 3 painters: Alice, Bob, and Carol. We have the following information:• Alice put in 15 paintings, 4% of her works have won first place.●Bob put in 5 paintings, 6% of his works have won first place.• Carol put in 10 paintings, 3% of her works have won first place.Multiple entries can win first place.(a) Suppose one of the entries is selected randomly. What is the probability that the entry wins first place?[Warning: We are not excluding the possibility of having only one first place winner, so it's not 30-1Round to 3 decimal places.20 sowate povapstallkola (8)(b) What is the probability that Alice will win first place? That is, if one of the entries wins first place,what is the probability the entry belongs to Alice? Round to 3 decimal places.wat oy bosqics n (alam()(c) What is the probability that a non-first place entry belongs to Bob? Round to 3 decimal places.ascule ambebs at when your boo

In this art competition featuring 30 entries from painters Alice, Bob, and Carol, we aim to analyze…

Answered: 5. An art competition has 30 entries…

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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An experiment is picking a card from a deck of 52 cards.SS = {2S, 3S, 4S, 5S, 6S, 7S, 8S, 9S, 10S, JS, QS, KS, AS, 2C, 3C, 4C, 5C, 6C, 7C, 8C, 9C, 10C, JC, QC, KC, AC, 2D, 3D, 4D, 5D, 6D, 7D, 8D, 9D, 10D, JD, QD, KD, AD, 2H, 3H, 4H, 5H, 6H, 7H, 8H, 9H, 10H, JH, QH, KH, AH}a. What is the probability that you chose a jack or a queen?P(a jack or a queen) = Give your answer as a reduced fraction.b. What is the probability that you chose a spade and a heart?P(a spade and a heart) = Give your answer as a reduced fraction.
In a class there are 4 students who are 19 years old and obtained 80 pints in the midterm. There are 6 students who are 19 years old and obtained 50 pints in the midterm. There are 6 students who are 20 years old and obtained 80 pints in the midterm. There are n students who are 20 years old and obtained 50 pints in the midterm. There are no other students. We randomly pick a student in the class, let their age be X and their score by Y. If we are given that X, Y are independent random variables, then compute n.
Suppose that in a survey of five-year-olds, 42% liked the letter A, 54% liked the letter B, and 47% liked the letter of C. 27% liked A and B, 25% liked A and C, 27% liked B and C, and 11% liked all of them. What percentage liked A and B but not the letter C?
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.
We survey 200 students, and ask each whether they like donuts, pizza, and/or tacos. Every student liked at least one of them. - 100 students liked donuts - 80 students liked pizza - 100 students liked tacos - 10 students liked all three options How many students liked exactly two of the options? Type your answer.
Cecil has blue, red, green, and black pens in his bag. This table shows how many of each type of pen he has in his bag. Pen Color Number ofPens Blue 6 Red 4 Green 2 Black 8 Cecil randomly chooses a pen from his bag. Which statement is true based on this data? A.The pen is 4 times more likely to be red than it is to be green. B.The pen is 3 times more likely to be blue than it is to be green. C.The pen is more likely to be blue than it is to be black. D.The pen is equally likely to be blue, red, green, or black.
In a survey, 200 restaurants were asked to select which of the following options were on their menu: tacos, burgers. 98 of the restaurants serve tacos and 74 of the restaurants serve burgers. 37 of the restaurants serve neither of these options. How many of the restaurants serve both tacos and burgers? Show your work.
You are trying frantically to get dressed, and you need to reach into your sock drawer to get two matching socks in the dark. Your sock drawer contains 20 socks, consisting of 10 matched pairs. All of them are only black or white, and they are loose, disorganized randomly, and not bound together. This means you have 10 black and 10 white socks in your disorganized drawer. This makes 10 total matching pairs of 5 pairs of white and 5 pairs of black. 1. How can you guarantee success of picking a matching pair? In other words, what is the minimum number of socks needing to be picked to guarantee a matching pair? (Hint: There is a right answer to this question!) 2. Explain dependent and independent trials
A father and his three children decide to hold a vote to select an after dinner activity. They will either see a play or a movie. If the majority of the family agrees on a preferred activity, then they will do that activity. If two family members vote to see a play and the other two family members vote to watch a movie, then (since the father will pay for the activity), the father's vote will be used to break the tie. (a) How many winning coalitions are there in this situation? (b) Find one of the children's Banzhaf power index.
Answer the questions below. (a) A certain committee consists of 17 people. From the committee, a president, a vice-president, and a treasurer are to be chosen. In how many ways can these 3 offices be filled? Assume that a committee member can hold at most one of these offices. (b) A company that makes crayons is trying to decide which 4 colors to include in a promotional mini-box of 4 crayons. The company can choose the 4 mini-box colors from its collection of 70 colors. How many mini-boxes are possible?

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