Question

two dice are rolled one after another. construct a sample space and determine the probability that the sum of the dots on the dice total a number greater than 2 if the second die is a 1.

the probability that the sum of the dots on the dice is a number greater than 2 if the second die is a 1 is .
(type an integer or a simplified fraction.)

Explanation:

Define the reduced sample space

$$ S = \{(1,1), (2,1), (3,1), (4,1), (5,1), (6,1)\} $$

Identify outcomes satisfying the condition

$$
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$$

Calculate the conditional probability

$$ P(\text{Sum} > 2 \mid \text{Second die is } 1) = \frac{5}{6} $$

Answer:

The probability that the sum of the dots on the dice is a number greater than 2 if the second die is a 1 is <blank>\(\frac{5}{6}\)</blank>.