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sweet-ann [11.9K]
1 year ago
11

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

nd time.
Mathematics
1 answer:
IceJOKER [234]1 year ago
8 0

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)=\frac{3}{6} \\ P(A)=\frac{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)=\frac{3}{6} \\ P(B)=\frac{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) = }\frac{1}{2}\cdot\frac{1}{2} \\ \text{ P(A and B) = }\frac{1}{4} \end{gathered}

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