3. Two standard dice are rolled. One is
yellow and the other is red. What is
the probability that the sum of the two
dice is 9, given that the yellow dice
landed on a 2?
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Answer :

To solve this problem, we can use the concept of conditional probability. We are given a condition, which is that the yellow die has landed on a number 2. Given this information, we need to determine the probability that the sum of the two dice is 9.

Since the yellow die has already landed on a 2, in order to achieve a sum of 9, the red die must land on a 7. However, a standard die only has the numbers 1 through 6 on its sides, so it is impossible for the red die to land on a 7.

Therefore, the conditional probability that the sum of the two dice is 9, given that the yellow die has landed on a 2, is 0 because no roll of the red die can satisfy this condition. There are no favorable outcomes out of the 6 possible outcomes of rolling the red die.

In mathematical terms, if [tex]\( Y \)[/tex] is the event that the yellow die is 2, and [tex]\( S \)[/tex] is the event that the sum is 9, then the probability we want to find is [tex]\( P(S|Y) \)[/tex]. Since there are no outcomes where both [tex]\( S \)[/tex] and [tex]\( Y \)[/tex] occur, [tex]\( P(S|Y) = 0 \)[/tex].