Question

Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6 the probability of getting a sum as 3 is

• A. \(\frac{1}{18}\)
• B. \(\frac{5}{18}\)
• C. \(\frac{1}{5}\)
• D. \(\frac{2}{5}\)

Answer 1

The Correct Option is C

When two dice are thrown, the possible sums are the results of adding the numbers on each die.
We are told that the sum of the numbers on the dice is less than 6.
Therefore, we are interested in the cases where the sum of the dice is 2, 3, 4, or 5.
The possible outcomes for these sums are: - Sum = 2: (1, 1)
Sum = 3: (1, 2), (2, 1)
Sum = 4: (1, 3), (2, 2), (3, 1)
Sum = 5: (1, 4), (2, 3), (3, 2), (4, 1)
Thus, there are 10 possible outcomes where the sum of the dice is less than 6. Out of these, the favorable outcomes for a sum of 3 are (1, 2) and (2, 1), which are 2 outcomes. Therefore, the probability of getting a sum of 3, given that the sum is less than 6, is: \[ \text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total possible outcomes}} = \frac{2}{10} = \frac{1}{5} \]

So, the correct answer is (C) : \(\frac{1}{5}\).