SOLUTION: 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 pr

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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