Question 1191823: Two dice are rolled and the sum of the outcomes is counted. (correct your answers to 4 decimal places.)
(a) Find the probability that the sum is divisible by 5.
(b) Find the probability that the sum is smaller than 4.
Answer by ikleyn(53763)   (Show Source):
You can put this solution on YOUR website! .
Two dice are rolled and the sum of the outcomes is counted. (correct your answers to 4 decimal places.)
(a) Find the probability that the sum is divisible by 5.
(b) Find the probability that the sum is smaller than 4.
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When two dice are rolling, there are 36 possible outcomes with the probability  each.
These outcomes are the pairs (a,b), where "a" and "b" are integer numbers from 1 to 6 inclusive.
(a) So, we need to count the number of all favorable outcomes.
Favorable outcomes are, obviously, those where the sum a+b is 5 or 10.
There are 4 possible outcomes with the sum of 5. They are (1,4), (2,3), (3,2) and (4,1).
Also, there are 3 possible outcomes with the sum of 10. They are (4,6), (5,5) and (6,4).
Thus, there are 4 + 3 = 7 favorable outcomes; therefore, the probability that the sum is divisible by 5 is  . ANSWER
(b) "the sum is smaller than 4" means that the sum is either 2 or 3.
There are 3 possible favorable outcomes (1,1), (1,2) and (2,1) with the sum 2 or 3.
Therefore, the probability that the sum is smaller than 4 is  =  . ANSWER
Solved.
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If you want to learn this subject and this class of problems BETTER, DEEPER and WIDER, look into the lesson
- Rolling a pair of fair dice
in this site. You will find there many other 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.
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