When rolling two standard six-sided dice, what is the probability that the sum of the dice will be even or a multiple of 3? (sho
w your work)
1 answer:
Answer:
2/3
Step-by-step explanation:
List all the possible sums. If it helps, make a table:
![\left[\begin{array}{ccccccc} &1&2&3&4&5&6\\1&2&3&4&5&6&7\\2&3&4&5&6&7&8\\3&4&5&6&7&8&9\\4&5&6&7&8&9&10\\5&6&7&8&9&10&11\\6&7&8&9&10&11&12\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccccc%7D%20%261%262%263%264%265%266%5C%5C1%262%263%264%265%266%267%5C%5C2%263%264%265%266%267%268%5C%5C3%264%265%266%267%268%269%5C%5C4%265%266%267%268%269%2610%5C%5C5%266%267%268%269%2610%2611%5C%5C6%267%268%269%2610%2611%2612%5Cend%7Barray%7D%5Cright%5D)
There are 36 total possible sums. Of those, 18 are even, and 6 are odd but multiples of 3.
Therefore, the probability is:
P = (18 + 6) / 36
P = 24 / 36
P = 2 / 3
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