Corrupted by their power, the judges running the popular game show America's NextTop Mathematician have been taking bribes from many of the contestants. Each episode,a given contestant is either allowed to stay on the show or is kicked off.If the contestant has been bribing the judges she will be allowed to stay with probability 1.If the contestant has not been bribing the judges, she will be allowed to stay with probability1/3.Suppose that 1/4 of the contestants have been bribing the judges. The same contestantsbribe the judges in both rounds, i.e., if a contestant bribes them in the first round, shebribes them in the second round too (and vice versa).(a) If you pick a random contestant who was allowed to stay during the first episode, whatis the probability that she was bribing the judges?(b) If you pick a random contestant, what is the probability that she is allowed to stayduring both of the first two episodes?

Answered: Image /qna-images/answer/90d311b8-29ef-4752-855d-b55392e8197e.jpg

Answered: Corrupted by their power, the judges…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question 6 Simon, Steven and 5 friends take 2 taxis. Each taxi has a maximum capacity of 4 passengers. (а) Find the number of possible arrangements if there are no restrictions. (b) Find the probability that Steven is in the taxi carrying 4 passengers.
Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to get to work on time. If he leaves now and does not get stopped by any traffic lights, he will arrive at work in exactly 8 minutes. In between his house and his work there are three traffic lights, A, B, and C. Each light that stops him will cause him to arrive an additional 2 minutes later. The following table displays the probability that he is stopped by each of the three traffic lights. Assume that the probability that he is stopped by any given light is independent of the probability that he is stopped by any other light. Traffic light A Traffic light B Traffic light C ?(?)P⁡(A) ?(?)P⁡(B) ?(?)P⁡(C) 0.6 0.4 0.9 What is the probability that the employee is not late for work? (Round to 3 decimal places)
QUESTION 9 Suppose a box contains 20 marbles, 6 are red, 5 are blue, and 9 are yellow. Find the requested probabilities. Leave your answer as an unsimplified fraction. a. If two marbles are selected with replacement, what is the probability that one is red and the other is yellow? (hint: order is not specific so you could choose a red then yellow or yellow then red). b. If two marbles are selected without replacement, what is the probability that one is red and the other is yellow? c. If 5 marbles are selected without replacement, what is the probability that they are all yellow?
Each of the questions in this boxpertains to rollinga pair of fair dice. Find the probability that the sum is less than 5 and the sum is prime.
At a local restaurant, you are allowed to pick one side with your dinner. Because you can only choose one, your side choice is mutually exclusive of all the other sides to chose from. On any given day, there is a 0.34 chance you will pick an fries, and a 0.1 chance you will pick an veggies. Today, you do not pick an veggies; what is the probability you pick fries today?
Could you do question 5?
We have two boxes, box A (6 blue marbles and 8 red marbles) and box B (6 blue marbles and 2 red marbles). We randomly pick one box, and randomly pick a marble from it. If the marble we picked was red, what is the probability that we drew from the first box?
At a museum cafe you can get a pre-made boxed lunch with a sandwich, fruit, and drink for only $3. • The sandwiches are made with either turkey or ham. • The fruit is either an apple or an orange. • The drink is either bottled water or juice. The number of boxes they make for every possible combination is the same. If you randomly choose one of the boxed lunches without knowing the contents, what is the probability you will get a turkey sandwich, an apple, and a bottle of water in your box? 1 4
Three friends agree to meet in one year if all are alive. What is the probability that of their meeting if their probabilities of being alive is 0.95, 0.88, and 0.96?

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