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?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 11CYU
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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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