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1. Two dice are tossed. The probability that the total score is a prime number is:

A. $\frac{1}{6}$

B. $\frac{5}{12}$

C. $\frac{1}{2}$

D. $\frac{7}{9}$

Solution:

Clearly, n(S) = (6 x 6) = 36
Let E = Event that the sum is a prime number.Then
E = {(1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3), (5, 2), (5, 6), (6, 1), (6, 5)}

\begin{aligned} ∴ n (E) = 15 \\ ∴ P (E) = \frac{n (E)}{n (S)} \\ = \frac{15}{36} \\ = \frac{5}{12} \end{aligned}

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