I have a probability question that is part of a Master's programme. The scenario is:
Two dice (one red, one blue) are tossed. What is the probability of scoring a total of exactly 6, given that the red die shows 4?
My thinking so far is that this is a conditional probability question. There are 5 possible ways two dice can total 6.
(Blue, Red) = (3, 3), (2, 5), (5, 2), (4, 2), (2, 4).
Of these, there is only one outcome in which Red shows 4.
I would assume that the result is then 1/36, but that is not the correct result.
Any help would be appreciated. Thank you.
Best Answer
You are given that the red die shows a $4$. Thus, the possible outcomes are $(1, 4), (2, 4), (3, 4), (4, 4), (5, 4), (6, 4)$, where the first entry in the ordered pair represents the outcome on the blue die and the second entry represents the outcome on the red die. Of these six outcomes that satisfy the condition that the red die displays a $4$, how many give a sum of $6$? Therefore, what is the probability of scoring exactly $6$ given that the red die shows a $4$?