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].
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].
