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Exercise 4. (a) Two people play a dice game. Each throws a regular 6 sided die. The perso with the largest number wins. (i) What is the probability that they throw exactly the same number (so no-one wins)? (ii) Calculate the probability that player 1 wins in two ways, (1.) using conditional probabilit conditioned on all the possible numbers that player 1 could throw, (2.) by arguing that, given th one player wins, then it must be player 1 or player 2 with equal probability. Check that your tw solution methods yield identical answers.

Exercise 4. (a) Two people play a dice game. Each throws a regular 6 sided die. The perso with the largest number wins. (i) What is the probability that they throw exactly the same number (so no-one wins)? (ii) Calculate the probability that player 1 wins in two ways, (1.) using conditional probabilit conditioned on all the possible numbers that player 1 could throw, (2.) by arguing that, given th one player wins, then it must be player 1 or player 2 with equal probability. Check that your tw solution methods yield identical answers.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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Exercise 4. (a) Two people play a dice game. Each throws a regular 6 sided die. The person with the largest number wins. (i) What is the probability that they throw exactly the same number (so no-one wins)? (ii) Calculate the probability that player 1 wins in two ways, (1.) using conditional probability, conditioned on all the possible numbers that player 1 could throw, (2.) by arguing that, given that one player wins, then it must be player 1 or player 2 with equal probability. Check that your two solution methods yield identical answers. 1 (b) Now suppose that Player 1 is throwing a 4 sided (tetrahedral) die and Player 2 is throwing a 6 sided (cube) die. (i) How many possible outcomes are there for Player 1's score and Player's 2 score. (ii) What is the probability that the two players throw the exact same number. (iii) Use conditional probability to calculate the probability that Player 1 wins.
Transcribed Image Text:Exercise 4. (a) Two people play a dice game. Each throws a regular 6 sided die. The person with the largest number wins. (i) What is the probability that they throw exactly the same number (so no-one wins)? (ii) Calculate the probability that player 1 wins in two ways, (1.) using conditional probability, conditioned on all the possible numbers that player 1 could throw, (2.) by arguing that, given that one player wins, then it must be player 1 or player 2 with equal probability. Check that your two solution methods yield identical answers. 1 (b) Now suppose that Player 1 is throwing a 4 sided (tetrahedral) die and Player 2 is throwing a 6 sided (cube) die. (i) How many possible outcomes are there for Player 1's score and Player's 2 score. (ii) What is the probability that the two players throw the exact same number. (iii) Use conditional probability to calculate the probability that Player 1 wins.
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