2. Use Bayes' theorem to solve the following: There are two bags. Thefirst bag contains four mangoes and two apples; the second bag containsfour mangoes and four apples. We also have a biased coin, which shows"Heads" with probability 0.6 and "Tails" with probability 0.4. If thecoin shows "Heads". we pick a fruit at random from bag 1; otherwisewe pick a fruit at random from bag 2. Your friend flips the coin (youcannot see the result), picks a fruit at random from the correspondingbag, and presents you a mango.What is the probability that the mango was picked from bag 2?

Solution : Given that : from Bayes theorem P(bag 2 given mango)=P(bag 2 and mango)/P(mango)…

Answered: 2. Use Bayes' theorem to solve 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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Consider the Monty Hall gameshow problem. Contestants are given the option of picking 1 out of 3 doors, one door has a car behind it and the other 2 doors have goats. The contestant notices Monty has a physical tell that could indicate what prize is behind the door the contestant chooses. If the contestant initially chooses the door with the car, Monty will arch his left eyebrow with probability 4/5. If the contestant initially chooses a door with a goat, Monty will arch his eyebrow in the sameway with probability 1/4. (a) For each of the two strategies for the contestant - to switch or remain with their chosen door- draw a tree diagram to represent this variation of the Monty Hall problem. (b) Assuming the location of the car and the contestant's initial choice are both chosen uniformly at random, what is the probability that Monty gives his physical tell? (c) Suppose you are selected to be the next contestant on Monty Hall. You decide to go with the following strategy: If Monty…
2. There are two boxes. Box A has 3 white chips and 1 red chip, Box B has 2 white chips and 1 red chip. There is a 40% chance that Box A will be the first box selected (that is, there is a 60% chance that Box B will be selected first.) A box is chosen at random. From the first box chosen, a chip is selected at random, the color is observed, and then the chip is placed in the other box (the one not chosen first). A chip is then selected at random from the other box and the color is observed. a. C. Find the probability of observing 2 red chips in a row. b. Find the probability of observing a white chip from the other box (the last box chosen). Given that one observes a white chip from the other box, find the probability that Box A was the first box chosen.
1. On the wheel shown here, what is the most likely outcome? llows azud on No prize Big No prize Big Small No p Small Big p OA. Big prize OB. Small prize OC. No prize OD. All outcomes are equally likely
4. A person answers each of three multiple choice questions at random. If there are four possible choices on each question with exactly one correct answer, what is the conditional probability that all three answers are correct given that at least one is correct?.
2.
11. As a small business owner, you decide to randomly give two of your loyal customers a $100 gift card each. To decide who gets the gift cards, you write down the names of each loyal customer and draw them out of a hat. You draw two names without replacement so that one person does not get both $100 gift cards. Of the 6 loyal customers you have, 3 live in Georgia. What is the probability that both of the $100 gift cards go to a loyal customer living in Georgia? .2 O.25 O.3 O none of the above are correct
Problem 12 25% of likely U.S. voters think that it is too easy to vote in the United States. You randomly select five likely U.S. voters. Find the probability that the number of likely U.S. voters who think that it is too easy to vote in the United States is a) Exactly two. b) At least two. c) Less than four.

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