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Judah is very fond of candies; he always has a few in his pockets. To add variety to his candy consumption, he plays a game to choose them. In his left pocket, he puts 5 orange and 3 strawberry candies, and in the right, he puts 4 orange and 2 strawberry. He then flips a fair coin and if it lands with tails showing, he draws a candy from the left pocket, and if it lands with heads showing, he picks one from his right pocket. (a) What is the probability that after two flips, he ended up eating two candies with the same flavor? (b) He gets back home and empties his pockets on the table. His mother, aware of his game, finds 7 orange candies and 5 strawberry candies. Help her figure out the sequence of the two coin flips with the highest probability that John obtained (by doing some Math-y Bayes' Theorem stuff!). (c) The next day, Judah has no more orange candies, so he fills his left pocket with 5 and his right pocket with 2 strawberry candies. He then goes to the grocery store to buy some orange candies. Knowing that he will put them all in his right pocket, how many must he buy so that on the next flip, he has (is as close as possible) to having as the same chance of drawing an orange candy as he has of drawing strawberry candy?

Judah is very fond of candies; he always has a few in his pockets. To add variety to his candy consumption, he plays a game to choose them. In his left pocket, he puts 5 orange and 3 strawberry candies, and in the right, he puts 4 orange and 2 strawberry. He then flips a fair coin and if it lands with tails showing, he draws a candy from the left pocket, and if it lands with heads showing, he picks one from his right pocket. (a) What is the probability that after two flips, he ended up eating two candies with the same flavor? (b) He gets back home and empties his pockets on the table. His mother, aware of his game, finds 7 orange candies and 5 strawberry candies. Help her figure out the sequence of the two coin flips with the highest probability that John obtained (by doing some Math-y Bayes' Theorem stuff!). (c) The next day, Judah has no more orange candies, so he fills his left pocket with 5 and his right pocket with 2 strawberry candies. He then goes to the grocery store to buy some orange candies. Knowing that he will put them all in his right pocket, how many must he buy so that on the next flip, he has (is as close as possible) to having as the same chance of drawing an orange candy as he has of drawing strawberry candy?

A First Course in Probability (10th Edition)
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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Judah is very fond of candies; he always has a few in his pockets. To add variety to his candy consumption, he plays a game to choose them. In his left pocket, he puts 5 orange and 3 strawberry candies, and in the right, he puts 4 orange and 2 strawberry. He then flips a fair coin and if it lands with tails showing, he draws a candy from the left pocket, and if it lands with heads showing, he picks one from his right pocket. (a) What is the probability that after two flips, he ended up eating two candies with the same flavor? (b) He gets back home and empties his pockets on the table. His mother, aware of his game, finds 7 orange candies and 5 strawberry candies. Help her figure out the sequence of the two coin flips with the highest probability that John obtained (by doing some Math-y Bayes' Theorem stuff!). (c) The next day, Judah has no more orange candies, so he fills his left pocket with 5 and his right pocket with 2 strawberry candies. He then goes to the grocery store to buy some orange candies. Knowing that he will put them all in his right pocket, how many must he buy so that on the next flip, he has (is as close as possible) to having as the same chance of drawing an orange candy as he has of drawing strawberry candy?
Transcribed Image Text:Judah is very fond of candies; he always has a few in his pockets. To add variety to his candy consumption, he plays a game to choose them. In his left pocket, he puts 5 orange and 3 strawberry candies, and in the right, he puts 4 orange and 2 strawberry. He then flips a fair coin and if it lands with tails showing, he draws a candy from the left pocket, and if it lands with heads showing, he picks one from his right pocket. (a) What is the probability that after two flips, he ended up eating two candies with the same flavor? (b) He gets back home and empties his pockets on the table. His mother, aware of his game, finds 7 orange candies and 5 strawberry candies. Help her figure out the sequence of the two coin flips with the highest probability that John obtained (by doing some Math-y Bayes' Theorem stuff!). (c) The next day, Judah has no more orange candies, so he fills his left pocket with 5 and his right pocket with 2 strawberry candies. He then goes to the grocery store to buy some orange candies. Knowing that he will put them all in his right pocket, how many must he buy so that on the next flip, he has (is as close as possible) to having as the same chance of drawing an orange candy as he has of drawing strawberry candy?
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