Final answer:
The probability that the score on the first die is 6 or the score on the second die is 5 when two fair six-sided dice are thrown is 11/36 . This is calculated by adding the probabilities of each event separately and then subtracting the overlap to avoid double-counting the scenario where both events occur.
Step-by-step explanation:
The question involves calculating the probability that the score on the first die is 6 or the score on the second die is 5 when two fair six-sided dice are thrown. To determine this probability, we consider the two scenarios separately and then combine them to find the total probability of either event occurring.
Calculating Probability
There are 36 possible outcomes when two dice are thrown, as each die has six faces, so the sample space has 6 x 6 = 36 outcomes.
The first scenario involves the first die showing a 6, which can happen in 6 different ways (since the second die can be any number from 1 to 6). The probability here is 6/36.
The second scenario involves the second die showing a 5. Again, this can happen in 6 different ways (with the first die being any number from 1 to 6). The probability for this scenario is also 6/36.
However, there is an overlap in these scenarios because both conditions are met when the first die is 6 and the second is 5. This outcome has been counted in both scenarios. So, we need to subtract this overlap from the total probability to avoid double-counting. There is 1 outcome where this overlap occurs. Therefore, we subtract 1/36 from the combined probability.
The total probability is the sum of the individual probabilities minus the overlap:
6/36 + 6/36 - 1/36 = 11/36
The correct option for the final answer is 11/36.
With this calculation, we find that the probability of either the first die showing a 6 or the second die showing a 5 is 11/36.