Two fair dice are rolled together. What is the probability of getting the sum of the numbers appearing on their tops as 6 and one of the dice shows number 2 on its top?

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AAI Junior Assistant (Fire Service) Official Paper (Held On: 15 Nov, 2022 Shift 2)
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  1. \(\frac{1}{18}\)
  2. \(\frac{1}{9}\)
  3. \(\frac{4}{9}\)
  4. \(\frac{1}{6}\)

Answer (Detailed Solution Below)

Option 1 : \(\frac{1}{18}\)
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Detailed Solution

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Given:

Two fair dice are rolled.

Sum of numbers = 6.

One die shows number 2.

Formula used:

Probability = Number of favorable outcomes / Total number of outcomes

Calculation:

Total number of outcomes when two dice are rolled = 6 × 6 = 36

Favorable outcomes:

Pairs with sum 6 and one die showing 2 is

(2, 4)

(4, 2)

Number of favorable outcomes = 2

Now,

Probability = 2 / 36 = 1 / 18

∴ The probability is 1/18.

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