Question

Two dice are thrown. What is the conditional probability of a total score of at least 8, given
that one of the dice has thrown 4?

Answer 1

1. Two dice are thrown. What is the conditional probability of a total score of at least 8, given that one of the dice has thrown 4?

**Solution.**

Let A means an event which occur when one of the (first) dice has thrown 4.

Let B means an event which occur when total score of at least 8.

Let $s_1$ - the number of points obtained by the roll of the first dice and $s_2$ - by the second dice.

$$P(A|B) = P(s_1 + s_2 \geq 8 | s_1 = 4) = P(s_1 + 4 \geq 8) = P(s_1 \geq 4), \text{ then}$$ $$P(A|B) = P(s_1 = 4) + P(s_1 = 5) + P(s_1 = 6) = \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = 0.5$$

**Answer: 0.5**