SOLUTION: Suppose you roll a pair of six-sided dice and add their totals. 1. What is the probability that the sum of the numbers on your dice is an even number or a number less than 6?

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Question 1193150: Suppose you roll a pair of six-sided dice and add their totals.
1. What is the probability that the sum of the numbers on your dice is an even number or a number less than 6?
2. What is the probability that the sum of the numbers on your dice is a prime number or a number greater than 5?
Found 2 solutions by ikleyn, Frederick94:
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
Suppose you roll a pair of six-sided dice and add their totals.
1. What is the probability that the sum of the numbers on your dice is an even number or a number less than 6?
2. What is the probability that the sum of the numbers on your dice is a prime number or a number greater than 5?
~~~~~~~~~~~~~~


                    Solution to part  (1) 


When rolling a pair of dice, there are 36 possible outcomes, in all, each with probability of  .


Of them, favorable are those pairs where the sum of numbers is 2, 3, 4, 5, 6, 8, 10 or 12.


    With the sum of  2, there is  1 pair,   (1,1).

    With the sum of  3, there are 2 pairs.  (1,2) and (2,1).

    With the sum of  4, there are 3 pairs.  (1,3), (2,2), (3,1).

    With the sum of  5, there are 4 pairs.

    With the sum of  6, there are 5 pairs.

    With the sum of  8, there are 5 pairs.

    With the sum of 10, there are 3 pairs.

    With the sum of 12, there is  1 pair.


In total, there are  1 + 2 + 3 + 4 + 5 + 5 + 3 + 1 = 24 favorable pairs.


So the probability is  p =  = .

Solved.

Solve the other part of the problem in a similar way.

---------------

If you want to learn nore about this subject and this class of problems,  look into the lesson
    - Rolling a pair of fair dice
in this site.  You will find there many similar solved problems.


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic  "Solved problems on Probability".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.



Answer by Frederick94(1)   (Show Source): You can put this solution on YOUR website!
Solution 2.
Prime Numbers Pair
2 1
3 2
5 4
7 6
11 2

Total 15 pairs
Sum of numbers greater than 5 Pair
6 5
8 5
9 4
10 3
12 1
Total 18 pairs
In total, there are 15 + 18 = 33 favorable pairs
Therefore, Probability P = 33/36 = 11/12
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