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} $.
-What is probability that neither X nor Y will occur?
A)$\frac{29}{26}$

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

C)$\frac{28}{36}$

D)$\frac{21}{36}$

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} $. 
-What is probability that neither X nor Y will occur?
A)$\frac{29}{26}$

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

C)$\frac{28}{36}$

D)$\frac{21}{36}$

Quizplus · Accepted Answer

The probability that neither X nor Y will occur is calculated as 1 minus the probability that either X or Y occurs. The probability of X occurring is $ \frac{5}{36} + \frac{2}{36} = \frac{7}{36} $. The probability of Y occurring is $ \frac{1}{36} + \frac{4}{36} + \frac{3}{36} = \frac{8}{36} $. The probability of either X or Y occurring is $ \frac{7}{36} + \frac{8}{36} = \frac{15}{36} $. Therefore, the probability that neither X nor Y will occur is $ 1 - \frac{15}{36} = \frac{21}{36} $.

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