Question:
Two fair cubical dice with faces numbered from 1 to 6 are rolled. What is the probability that the sum of the numbers on the two faces that appear on the top is 8, given that each of the two faces that appear on the top shows an odd number?
Two fair cubical dice with faces numbered from 1 to 6 are rolled. What is the probability that the sum of the numbers on the two faces that appear on the top is 8, given that each of the two faces that appear on the top shows an odd number?
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In conditional probability:
- Restrict sample space first
- Then find favourable cases
Updated On: May 13, 2026
- $\frac{1}{18}$
- $\frac{2}{9}$
- $\frac{5}{36}$
- $\frac{1}{9}$
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The Correct Option is D
Solution and Explanation
Concept:
Conditional probability:
\[
P(A|B) = \frac{\text{Favourable outcomes}}{\text{Total outcomes under condition}}
\]
Step 1: List odd numbers.
Odd numbers on a die: $\{1,3,5\}$
Step 2: Total possible outcomes (both odd).
\[ 3 \times 3 = 9 \text{ outcomes} \] These are: \[ (1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5) \]
Step 3: Find favourable outcomes (sum = 8).
\[ (3,5), (5,3) \] Number of favourable outcomes = 2
Step 4: Compute probability.
\[ P = \frac{2}{9} \]
Step 5: Final conclusion.
Thus, the required probability is: \[ $\frac{2{9}$} \]
Step 1: List odd numbers.
Odd numbers on a die: $\{1,3,5\}$
Step 2: Total possible outcomes (both odd).
\[ 3 \times 3 = 9 \text{ outcomes} \] These are: \[ (1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5) \]
Step 3: Find favourable outcomes (sum = 8).
\[ (3,5), (5,3) \] Number of favourable outcomes = 2
Step 4: Compute probability.
\[ P = \frac{2}{9} \]
Step 5: Final conclusion.
Thus, the required probability is: \[ $\frac{2{9}$} \]
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