Question

A die was thrown twice and it was found that the sum of the numbers that appeared was 6. Find the conditional probability that the number 4 appeared at least once.

Hint:

For conditional probability, count the favorable outcomes and divide by the total number of possible outcomes.

Answer 1

Step 1: The possible outcomes when a die is thrown twice and the sum is 6 are: \[ (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) \] So, there are 5 outcomes in total. Step 2: The favorable outcomes for the number 4 to appear at least once are: \[ (2, 4), (4, 2) \] So, there are 2 favorable outcomes. 

Step 3: The conditional probability is given by: \[ P({4 appears at least once}) = \frac{{Number of favorable outcomes}}{{Total number of outcomes}} = \frac{2}{5} \] Thus, the conditional probability is \( \frac{2}{5} \).