Question

chapter 4.2 homework
score: 51/83 answered: 31/38
question 32
4.2 theoretical probability. mutually exclusive/not mutually exclusive.
a die is rolled twice. what is the probability of showing a 2 on both rolls? type as a fraction or round to four decimal places.
your answer is:
question help: video message instructor

Explanation:

Step1: Determine probability of one - roll

The probability of rolling a 2 on a single fair six - sided die is $\frac{1}{6}$ since there is 1 favorable outcome (rolling a 2) out of 6 possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).

Step2: Use multiplication rule for independent events

Since the two die - rolls are independent events, the probability of two independent events $A$ and $B$ both occurring is $P(A\cap B)=P(A)\times P(B)$. Here, $A$ is the event of rolling a 2 on the first roll and $B$ is the event of rolling a 2 on the second roll. So the probability of rolling a 2 on both rolls is $\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}$.

Step3: Convert to decimal

$\frac{1}{36}\approx0.0278$ (rounded to four decimal places).

Answer:

$0.0278$