Use the data given below to answer the following question(s).
In an event $ X $, the probability of rolling a sum of 8 on two dice is $ \frac{5}{36} $ while the probability of rolling an 11 is $ \frac{2}{36} $. In another event $ Y $, the probability of rolling a 2 is $ \frac{1}{36} $, the probability of rolling a 9 is $ \frac{4}{36} $, and the probability of rolling a 4 is $ \frac{3}{36} $.
-What is the probability that either event X or Y occurs?

A)$\frac{8}{36}$

B)$\frac{15}{36}$

C)$\frac{7}{36}$

D)$\frac{1}{36}$

Question

Use the data given below to answer the following question(s).
In an event $ X $, the probability of rolling a sum of 8 on two dice is $ \frac{5}{36} $ while the probability of rolling an 11 is $ \frac{2}{36} $. In another event $ Y $, the probability of rolling a 2 is $ \frac{1}{36} $, the probability of rolling a 9 is $ \frac{4}{36} $, and the probability of rolling a 4 is $ \frac{3}{36} $. 
-What is the probability that either event X or Y occurs?

A)$\frac{8}{36}$

B)$\frac{15}{36}$

C)$\frac{7}{36}$

D)$\frac{1}{36}$

Quizplus · Accepted Answer

To find the probability that either event X or Y occurs, we need to add the probabilities of the two events and subtract the probability of both events occurring at the same time (since this would be double counting). 
The probability of event X occurring is $ \frac{5}{36} + \frac{2}{36} = \frac{7}{36} $. 
The probability of event Y occurring is $ \frac{1}{36} + \frac{4}{36} + \frac{3}{36} = \frac{8}{36} $. 
Since the two events involve different outcomes (i.e. rolling a sum of 8 or 11 on two dice is different from rolling a 2, 4, or 9), they are mutually exclusive, and so the probability of both occurring at the same time is 0. 
Therefore, the probability of either event X or Y occurring is $ \frac{7}{36} + \frac{8}{36} - 0 = \frac{15}{36} $, which simplifies to $ \frac{5}{12} $.

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