Question

A single die is rolled twice. Find the probability of rolling an even number the first time and a number greater than 3 the second time.

Answer 1

Events

• A: an even number is rolled in the first time

,

• B: a number greater than 3 is rolled the second time

The probability of rolling an even number is:

`\begin{gathered} P(A)=\frac{\text{ number of favorable outcomes}}{\text{ total possible outcomes}} \\ P(A)=(3)/(6) \\ P(A)=(1)/(2) \end{gathered}`

The probability of rolling a number greater than 3 is:

`\begin{gathered} P(B)=\frac{\text{ number of favorable outcomes}}{\text{ total possible outcomes}} \\ P(B)=(3)/(6) \\ P(B)=(1)/(2) \end{gathered}`

Events A and B are independent, then the probability of one happening after the other is:

`\begin{gathered} \text{ P(A and B) = }P(A)\cdot P(B) \\ \text{ Substituting with the values previously found:} \\ \text{ P(A and B) = }(1)/(2)\cdot(1)/(2) \\ \text{ P(A and B) = }(1)/(4) \end{gathered}`