SOLUTION: A pair of dice is rolled together till a sum of either 5 or 7 is obtained. Then probability that 5 comes before 7
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Question 1132192: A pair of dice is rolled together till a sum of either 5 or 7 is obtained. Then probability that 5 comes before 7 Found 2 solutions by greenestamps, ikleyn:Answer by greenestamps(13200) (Show Source):
P(5 before 7) =
P((5 on first flip) OR
(neither 5 nor 7 on first flip AND 5 on second flip) OR
(neither 5 nor 7 on first flip AND neither 5 nor 7 on second flip AND 5 on third flip) OR
...) =
1/9 + (13/18)(1/9) + (13/18)(13/18)(1/9) + ...
This is an infinite geometric series with first term a = 1/9 and common ratio r = 13/18.
The formula for the sum of an infinite geometric series with first term a and common ratio r (|r|<1) is
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A pair of dice is rolled together till a sum of either 5 or 7 is obtained. Then probability that 5 comes before 7
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As I read the problem, I understand it in this way (literally as it is written) :
A pair of dice is rolled together. As soon as a sum of either 5 or 7 is obtained, the experiment stops.
What is the probability that the last obtained sum is 5 ?
It is different from reading by @greenestamps, who counts when and how the "7" will be obtained after getting of "5".
In my interpretation, I do not concern what will happen after EITHER 5 OR 7 will be obtained - it is the command
to stop the experiment.
Therefore, my solution is different, although the answer is the same number.
Solution
P(5) = = <<<---=== of 6x6 = 36 sample cases only 4 produce the sum of 5.
P(7) = = <<<---=== of 6x6 = 36 sample cases only 6 produce the sum of 7.
The problem asks to find a conditional probability of getting the sum of 5 under the condition that this sum is EITHER "5" OR "7".
Then this conditional probability is = = = = 0.4 = 40%. ANSWER
