Question

A pair of fair dice are rolled together. The probability of getting a total of 8 is

• A. \( \frac{1}{9} \)
• B. \( \frac{5}{36} \)
• C. \( \frac{7}{36} \)
• D. \( \frac{11}{36} \)
• E. \( \frac{1}{36} \)

Hint:

For two-dice probability questions: Always remember: \[ \text{Total outcomes} = 36 \] Then list the favourable ordered pairs carefully. Do not miss pairs like \((2,6)\) and \((6,2)\), since both are counted separately.

Answer 1

The Correct Option is B

Concept: When two fair dice are rolled together: \[ \text{Total number of possible outcomes} = 6 \times 6 = 36 \] because each die has 6 possible outcomes. Probability is calculated using: \[ P(E) = \frac{ \text{Number of favourable outcomes} }{ \text{Total number of possible outcomes} } \] So first, we find all outcomes whose sum is 8.

Step 1: Find the total number of outcomes. Each die has outcomes: \[ 1,2,3,4,5,6 \] Thus, for two dice: \[ \text{Total outcomes} = 6 \times 6 = 36 \] So, \[ n(S)=36 \] where \(S\) is the sample space.

Step 2: Find favourable outcomes for sum = 8. We need: \[ \text{First die} + \text{Second die} = 8 \] Possible ordered pairs are: \[ (2,6) \] \[ (3,5) \] \[ (4,4) \] \[ (5,3) \] \[ (6,2) \] Thus, number of favourable outcomes: \[ n(E)=5 \]

Step 3: Apply probability formula. \[ P(\text{sum } = 8) = \frac{5}{36} \] Therefore, \[ \boxed{ P = \frac{5}{36} } \] Hence, the correct option is: \[ \boxed{(B)\ \frac{5}{36}} \]