Question

question 33 4.2 theoretical probability. mutually exclusive/not mutually exclusive. a die is rolled twice. what is the probability of showing a 3 on the first roll and an even number on the second roll? write as a fraction or round to four decimal places. your answer is : question help: video message instructor

Explanation:

Step1: Find probability of first - roll event

The probability of rolling a 3 on the first roll of a fair six - sided die. A fair die has 6 possible outcomes. The probability of getting a 3 is $P(3)=\frac{1}{6}$ since there is 1 favorable outcome (rolling a 3) out of 6 total outcomes.

Step2: Find probability of second - roll event

The probability of rolling an even number (2, 4, or 6) on the second roll of a fair six - sided die. There are 3 favorable outcomes (2, 4, 6) out of 6 total outcomes. So the probability of rolling an even number is $P(\text{even})=\frac{3}{6}=\frac{1}{2}$.

Step3: Use multiplication rule for independent events

Since the two rolls of the die are independent events (the outcome of the first roll does not affect the outcome of the second roll), the probability of both events occurring is the product of their individual probabilities. So $P(3\text{ on first},\text{ even on second}) = P(3)\times P(\text{even})$.
Substitute the values: $\frac{1}{6}\times\frac{1}{2}=\frac{1}{12}\approx0.0833$.

Answer:

$\frac{1}{12}\approx0.0833$