Question

a six - sided number cube is rolled twice. which expression can be used to find ( p(5,\text{ then }3) )?
( \frac{1}{5}cdot\frac{1}{3} )
( \frac{1}{6}cdot\frac{1}{5} )
( \frac{5}{6}cdot\frac{3}{6} )
( \frac{1}{6}cdot\frac{1}{6} )

Explanation:

Step1: Calculate the probability of rolling a 5

The probability of rolling a 5 on a six - sided number cube is \(P(5)=\frac{1}{6}\) (since there is 1 favorable outcome (rolling a 5) out of 6 possible outcomes (1, 2, 3, 4, 5, 6)).

Step2: Calculate the probability of rolling a 3

The probability of rolling a 3 on a six - sided number cube is \(P(3)=\frac{1}{6}\) (since there is 1 favorable outcome (rolling a 3) out of 6 possible outcomes (1, 2, 3, 4, 5, 6)).

Step3: Use the multiplication rule for independent events

Since the two rolls of the number cube are independent events (the outcome of the first roll does not affect the outcome of the second roll), the probability of rolling a 5 then a 3 is \(P(5\text{ then }3)=P(5)\times P(3)\). Substituting the values from Step 1 and Step 2, we get \(P(5\text{ then }3)=\frac{1}{6}\times\frac{1}{6}\).

Answer:

\(\frac{1}{6}\cdot\frac{1}{6}\) (the fourth option)