A pair of dice is rolled, and the number that appears uppermost on each die is observed.
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A pair of dice is rolled, and the number that appears uppermost on each die is observed.

[From: ] [author: ] [Date: 12-04-01] [Hit: ]
Refer to this experiment and find the probability of the given event. (Enter your answer as a fraction.(b) A double is thrown.(c) The sum of the numbers is at least 4.-Well, there are 36 possible outcomes for the denominator.......
I'm having trouble with these three portions of a question.

A pair of dice is rolled, and the number that appears uppermost on each die is observed.Refer to this experiment and find the probability of the given event. (Enter your answer as a fraction.)

(a) The sum of the numbers is either 7 or 11

(b) A double is thrown.

(c) The sum of the numbers is at least 4.

-
Well, there are 36 possible outcomes for the denominator.

(a)
We have (3,4),(4,3),(2,5),(5,2),(6,1),(1,6) for 7
We have (6,5),(5,6) for 11

All together it is 8 ways so 8/36 = 2/9

(b)
A double would be (1,1),(2,2)...(6,6) so the answer is 6/36 = 1/6

(c)
Because the there are so many more numbers that fit then don't, I am going to solve for the opposite and subtract from one. So we are looking for the sum of numbers smaller than 4.

(1,1),(1,2),(2,1) = 3, so the answer is 1 - 3/36 = 36/36 - 3/36 = 33/36
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