Question

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. $\frac{7}{9}$

Hint:

Always list all possible sums when dealing with dice probability questions.

Answer 1

The Correct Option is B

Step 1: Identify possible outcomes.
When two dice are tossed, the total number of possible outcomes is $6 \times 6 = 36$.
Step 2: Identify prime sums.
Possible prime sums are $2, 3, 5, 7, 11$.
Step 3: Count favorable outcomes.
Sum = 2 $\rightarrow$ 1 outcome
Sum = 3 $\rightarrow$ 2 outcomes
Sum = 5 $\rightarrow$ 4 outcomes
Sum = 7 $\rightarrow$ 6 outcomes
Sum = 11 $\rightarrow$ 2 outcomes
Total favorable outcomes = $1 + 2 + 4 + 6 + 2 = 15$.
Step 4: Calculate probability.
\[ P = \frac{15}{36} = \frac{5}{12} \]