Question 1191823
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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   {{{1/36}}}   each.

These outcomes are the pairs  (a,b),  where  "a"  and  "b"  are integer numbers from  1  to  6  inclusive.



<pre>
(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 {{{7/36}}}.    <U>ANSWER</U>



(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  {{{3/36}}} = {{{1/12}}}.    <U>ANSWER</U>
</pre>

Solved.


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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Rolling-a-pair-of-fair-dice.lesson>Rolling a pair of fair dice</A> 

in this site. &nbsp;You will find there many other similar solved problems.


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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic &nbsp;"<U>Solved problems on Probability</U>". 



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