To find the probability that the first die is a 2 OR the sum is 5, we need to find the probability of each event separately and then add them together.
1. Probability that the first die is a 2:
There are 6 possible outcomes for the second die, so the total number of outcomes where the first die is a 2 is 6.
Therefore, the probability that the first die is a 2 is \( \frac{1}{6} \).
2. Probability that the sum is 5:
There are four combinations that give a sum of 5: (1, 4), (2, 3), (3, 2), and (4, 1).
Therefore, the probability that the sum is 5 is \( \frac{4}{36} = \frac{1}{9} \).
Now, we add the probabilities together:
\[ P(\text{first die is 2 OR sum is 5}) = P(\text{first die is 2}) + P(\text{sum is 5}) \]
\[ P(\text{first die is 2 OR sum is 5}) = \frac{1}{6} + \frac{1}{9} \]
\[ P(\text{first die is 2 OR sum is 5}) = \frac{3}{18} + \frac{2}{18} \]
\[ P(\text{first die is 2 OR sum is 5}) = \frac{5}{18} \]
So, the probability that the first die is a 2 OR the sum is 5 is \( \frac{5}{18} \).
