SOLUTION: A die is rolled twice. What is the probability that the sum of the rolls is less than 4 given that one of the rolls is a 1?

Algebra ->  Probability-and-statistics -> SOLUTION: A die is rolled twice. What is the probability that the sum of the rolls is less than 4 given that one of the rolls is a 1?      Log On


   



Question 1118482: A die is rolled twice. What is the probability that the sum of the rolls is less than 4 given that one of the rolls is a 1?
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Let +S%5B3%5D+ = event that the sum is less than 4 (3 for "3 or less")
Let ++D%5B1%5D+ = event that (at least) one die is a 1
P(+S%5B3%5D+ |D%5B1%5D) * P(D%5B1%5D) = P(D%5B1%5DS%5B3%5D)
P(D%5B1%5D) = 11/36
P(D%5B1%5DS%5B3%5D) = 3/36
so
P(+S%5B3%5D+) = (3/36) / (11//36) = +highlight%28matrix%281%2C3%2C+%22+%22%2C+3%2F11%2C+%22+%22%29%29+