Explanation Given: Three dice are rolled. If the first die shows 4 , find the probability that the sum of the three dice is less than 12 . Probability of an event E is the number of ways the event E can occur divided by the total number of possible outcomes. Mathematically it can be written as P ( E ) = n ( E ) n ( S ) where n ( E ) denotes the number of ways in which the event E can occur and n ( S ) denotes the total number of outcomes or the number of sample space. Let the probability that the first die shows 4 is P ( A ) and the probability that the sum of the three dice is less than 12 is P ( B ) . We have to find the probability that the sum of the dice is less than 12 if the probability that the first die shows a 4 . That means we have to find P ( B A ) . Formula used: Conditional Probability of an event B to occur while A is occurred is given by P ( B A ) = P ( B ∩ A ) P ( A ) . Calculation: Description P ( B A ) = P ( B ∩ A ) P ( A ) Step 1: Sample space S is the total outcomes of rolling three dice. It is too long to write all the outcomes of rolling a three dice. So we can use the formula of n ( S ) = 6 n where n denotes number of dice. By describing it we can find n ( S ) . n ( S ) = 6 3 = 216 \ Step 2: A be the event in which the first die shows 4 . By describing it we can find n ( A ) . n ( A ) = 36 Step 3: By substituting the above values in P ( A ) = n ( A ) n ( S ) , to find P ( A ) . P ( A ) = 36 216 Step 4: A be the event in which the first die shows 4 . B is the event in which the sum of the dice is less than 12 . By describing this we can find n ( A ∩ B ) . A ∩ B = { ( 4 , 1 , 1 ) , ( 4 , 1 , 2 ) , ( 4 , 1. 3 ) ...

College Algebra with Modeling & Visualization (5th Edition)

5th Edition

ISBN: 9780321826138

Author: Gary K. Rockswold

Publisher: PEARSON

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Chapter 8.6, Problem 70E

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Probability that the sum of the three dice is less than $12$ , if the first die shows a $4$ when three dice are rolled.

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Chapter 8.6, Problem 69E

Chapter 8.6, Problem 71E

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Chapter 8 Solutions

College Algebra with Modeling & Visualization (5th Edition)

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

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Probability that the sum of the three dice is less than 12 , if the first die shows a 4 when three dice are rolled.

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Probability that the sum of the three dice is less than 12, if the first die shows a 4 when three dice are rolled.

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Chapter 8 Solutions

Probability that the sum of the three dice is less than $12$ , if the first die shows a $4$ when three dice are rolled.