Question

a single die is rolled twice. find the probability of rolling a 4 the first time and a 2 the second time.

find the probability of rolling a 4 the first time and a 2 the second time.
(type an integer or a simplified fraction.)

Explanation:

Step1: Calculate the probability of rolling a 4

A die has 6 faces. The probability of rolling a 4 on a single - die roll is \(P(4)=\frac{1}{6}\) (since there is 1 favorable outcome out of 6 possible outcomes).

Step2: Calculate the probability of rolling a 2

The probability of rolling a 2 on a single - die roll is \(P(2)=\frac{1}{6}\) (since there is 1 favorable outcome out of 6 possible outcomes).

Step3: Use the multiplication rule for independent events

Since the two die rolls 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 \(P = P(4)\times P(2)\).
Substitute \(P(4)=\frac{1}{6}\) and \(P(2)=\frac{1}{6}\) into the formula: \(P=\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}\)

Answer:

\(\frac{1}{36}\)