Question 1201644: Find the probability that the sum is as stated when a pair of dice is rolled. (Enter your answers as fractions.)
A. even and doubles
B. even or doubles
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website!  .
The above shows the 36 outcomes when two dice are rolled
Pick up the conditions stated and find probability.
P= Number of possible outcomes/ Total number of outcomes.
Choose from above
Doubles (2,2),(4,4),(6,6)
P = 3/36 = 1/12
Doubles or even
You locate there are 24 outcomes
P = 24/36 =2/3
Answer by ikleyn(53547)  (Show Source):
You can put this solution on YOUR website! .
Find the probability that the sum is as stated when a pair of dice is rolled. (Enter your answers as fractions.)
A. even and doubles
B. even or doubles
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The answers and the logic in the post by @mananth both are incorrect for both (a) and (b).
I came to bring correct answers with explanations.
(a) even AND doubles.
The condition says to count the pairs that are doubles and have even sum.
This intersection of two conditions consists of 6 outcomes
(1,1), (2,2), (3,3), (4,4), (5,5) and (6,6).
Notice that under this condition, each double pair has an even sum.
So, in case (a) the probability is 6/36 = 1/6. <<<---=== ANSWER
(b) even or doubles
The number of outcomes with even sum is 36/2 = 18.
It is clear from symmetry.
All doubles have even sum, so they fall into the even category.
Thus, in case (b), the probability is 18/36 = 1/2. <<<---=== ANSWER
Solved correctly.
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A notice to the visitor / to the creator of this problem The problem formulation is provocatively incorrect.
A correct formulation should be like THIS
Find the probability that the conditions are satisfied when a pair of dice is rolled.
Professional Math writers NEVER create provocative formulations, because their goal is not to confuse, but, in opposite - to teach.
Provocative formulations are the product of those unprofessional writers, whose goal is to confuse, but not to teach.
Do you feel the difference ? ?
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