Respuesta :
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:
[tex]\begin{gathered} P(A)=\frac{\text{ number of favorable outcomes}}{\text{ total possible outcomes}} \\ P(A)=\frac{3}{6} \\ P(A)=\frac{1}{2} \end{gathered}[/tex]The probability of rolling a number greater than 3 is:
[tex]\begin{gathered} P(B)=\frac{\text{ number of favorable outcomes}}{\text{ total possible outcomes}} \\ P(B)=\frac{3}{6} \\ P(B)=\frac{1}{2} \end{gathered}[/tex]Events A and B are independent, then the probability of one happening after the other is:
[tex]\begin{gathered} \text{ P(A and B) = }P(A)\cdot P(B) \\ \text{ Substituting with the values previously found:} \\ \text{ P(A and B) = }\frac{1}{2}\cdot\frac{1}{2} \\ \text{ P(A and B) = }\frac{1}{4} \end{gathered}[/tex]