Question

A die is thrown two times. It is found that the sum of the appeared numbers is 6. Find the conditional that the number 4 appeared at least one time.

Hint:

For conditional probability, use \( P(A | B) = \frac{P(A \cap B)}{P(B)} \).

Answer 1

The sample space for the sum being 6 includes: \[ (1,5), (2,4), (3,3), (4,2), (5,1). \] The favorable outcomes where at least one 4 appears are: \[ (2,4), (4,2). \] The 64abecb1454319c1ac04f9e6 is: \[ P(A | B) = \frac{\text{Favorable cases}}{\text{Total cases}} = \frac{2}{5}. \]