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Please do this short answer question correctly We are going to roll 5 independent dice (like playing Yahtzee - but we will only roll once). The sum of the values of the dice can range anywhere from 5 (a roll of all 5 dice being a 1) to 30 (a roll of all 5 dice being a 6). I have determined that (to the 6th decimal) P(sum of values of the dice ≥ 8) = .997299. (i) Determine the P(sum of values of the dice ≤ 7) (to the 6th decimal). (ii) Provide a brief explanation as to the reason why your answer is correct.

Please do this short answer question correctly We are going to roll 5 independent dice (like playing Yahtzee - but we will only roll once). The sum of the values of the dice can range anywhere from 5 (a roll of all 5 dice being a 1) to 30 (a roll of all 5 dice being a 6). I have determined that (to the 6th decimal) P(sum of values of the dice ≥ 8) = .997299. (i) Determine the P(sum of values of the dice ≤ 7) (to the 6th decimal). (ii) Provide a brief explanation as to the reason why your answer is correct.

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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Please do this short answer question correctly We are going to roll 5 independent dice (like playing Yahtzee - but we will only roll once). The sum of the values of the dice can range anywhere from 5 (a roll of all 5 dice being a 1) to 30 (a roll of all 5 dice being a 6). I have determined that (to the 6th decimal) P(sum of values of the dice ≥ 8) = .997299. (i) Determine the P(sum of values of the dice ≤ 7) (to the 6th decimal). (ii) Provide a brief explanation as to the reason why your answer is correct.
Expert Solution
Step 1: Probability calculated.

There arte 5 dice.Each dice has 6 faces.Therfore the number of sample points is   6 to the power of 5 =7776

Let  X be the sum of faces of dice,then


Let A be the event  {X: X less or equal than 7} then A will contain (1,1,1,1,1) : 1 time giving X=5

                                                                              (1,1,1,1,2)  : fraction numerator 5 factorial over denominator 4 factorial space 1 factorial end fraction equals 5 times giving X=6

                                                                     and   (1,1,1,2,2)  :fraction numerator 5 factorial over denominator 3 factorial space 2 factorial end fraction =10  times giving X=7

Therefore

P(X less or equal than 7)=P(X=5)+P(X=6)+P(X=7) = (1+5+10)/7776 =16 over 7776= 0.002058

Moreover P(Xgreater or equal than8) = 1-P(X<8)= 1-P(Xless or equal than7)= 1- 0.002058 =0.997942, which does not match to your calculation.

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