Question 1094875: A four sided die is rolled. If the outcome is "1" or "2", you roll once more; otherwise you stop. What is the probability that the sum of rolls is >= 4?
Found 3 solutions by KMST, Edwin McCravy, AnlytcPhil:
Answer by KMST(5328)   (Show Source):
Answer by Edwin McCravy(20064)  (Show Source):
Answer by AnlytcPhil(1810)  (Show Source):
You can put this solution on YOUR website!
I'm thinking that's wrong and that you should make a probability
tree diagram of all possible outcomes, with the probability of
going along each branch (line) written on the branch:
The successful outcomes are boxed in red.
The probability of getting the highest highlighted 4 on the
right is to go along the branch from START to 1 (roll 1 first),
with probability 1/4, and then go along the branch from 1 to
the 4 (roll 4 second), with another probability of 1/4. So
the probability of getting the 4 by rolling a 1 first and then
a 4, is gotten by multiplying the 1/4 to go from START to 1, times
the 1/4 to go from the 1 to the 4. It is similar for the other
outcomes on the far right
So
the probability of the upper highlighted 4 is (1/4)(1/4) = 1/16.
the probability of the upper highlighted 5 is (1/4)(1/4) = 1/16.
the probability of the other highlighted 4 is (1/4)(1/4) = 1/16.
the probability of the other highlighted 5 is (1/4)(1/4) = 1/16.
the probability of the highlighted 6 is (1/4)(1/4) = 1/16.
plus
the probability of the highlighted 4 on the bottom, the case where
a 4 was rolled first and then you stopped is 1/4, so the desired
probability is the sum of all those probabilities:
1/16 + 1/16 + 1/16 + 1/6 + 1/16 + 1/4 = 9/16.
Edwin
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