Question:
A dice is thrown three times. If the first throw is five, the probability of getting 14 as the sum is:
A dice is thrown three times. If the first throw is five, the probability of getting 14 as the sum is:
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Reduce problem after fixing condition to simplify counting.
Updated On: Apr 30, 2026
- \(\frac{1}{9} \)
- \(\frac{1}{3} \)
- \(\frac{2}{9} \)
- \(\frac{2}{3} \)
- \(\frac{1}{5} \)
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The Correct Option is A
Solution and Explanation
Concept:
Conditional probability:
\[
P(A|B) = \frac{\text{favourable outcomes}}{\text{total outcomes}}
\]
Step 1: Fix first throw.
\[ \text{First number} = 5 \] Remaining sum needed: \[ 14 - 5 = 9 \]
Step 2: Find combinations.
Possible pairs: \[ (3,6), (4,5), (5,4), (6,3) \Rightarrow 4 \text{ outcomes} \]
Step 3: Total possible outcomes.
\[ 6 \times 6 = 36 \]
Step 4: Compute probability.
\[ \frac{4}{36} = \frac{1}{9} \]
Step 1: Fix first throw.
\[ \text{First number} = 5 \] Remaining sum needed: \[ 14 - 5 = 9 \]
Step 2: Find combinations.
Possible pairs: \[ (3,6), (4,5), (5,4), (6,3) \Rightarrow 4 \text{ outcomes} \]
Step 3: Total possible outcomes.
\[ 6 \times 6 = 36 \]
Step 4: Compute probability.
\[ \frac{4}{36} = \frac{1}{9} \]
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