Question

consider a six - sided die that has 1 dot on one side, 2 dots on two sides, and 3 dots on three sides. if the die is rolled twice, determine the probability of rolling a 2 and then a 1.
the probability of rolling a 2 and a 1 is □. (type an integer or a simplified fraction.)

Explanation:

Step1: Determine the probability of rolling a 2 on the first roll

The die has 6 sides. The probability of rolling a 2 on the first roll is $P(2)=\frac{2}{6}=\frac{1}{3}$ (since there are 2 sides with 2 - dots).

Step2: Determine the probability of rolling a 1 on the second roll

The probability of rolling a 1 on the second roll is $P(1)=\frac{1}{6}$ (since there is 1 side with 1 - dot).

Step3: Use the multiplication rule for independent events

For two independent events \(A\) and \(B\), \(P(A\cap B)=P(A)\times P(B)\). Here, \(A\) is the event of rolling a 2 and \(B\) is the event of rolling a 1. So \(P(2\cap1)=\frac{1}{3}\times\frac{1}{6}\).

$$P(2\cap1)=\frac{1\times1}{3\times6}=\frac{1}{18}$$

Answer:

\(\frac{1}{18}\)