Question

A dice is rolled twice. What is the probability of showing a 3 on the first dice or an odd number on the second roll? Round your answer to three decimal places.

Answer 1

The sample space of rolling a dice is

S = {1,2,3,4,5,6}

The probability of rolling a 3, based on the sample space, is 1 out 6 chances

P(3) = 1/6

The probability of rolling an odd number, based on the sample space are {1,3,5}, is 3 out of 6 chances.

P(odd) = 3/6

By counting principle, the probability of showing a 3 on the first dice, and and odd number on second roll is

`\begin{gathered} P(3\text{ then odd})=P(3)\cdot P(\text{odd}) \\ P(3\text{ then odd})=(1)/(6)\cdot(3)/(6) \\ P(3\text{ then odd})=(3)/(36) \\ P(3\text{ then odd})=0.083333\ldots \end{gathered}`

Rounding to three decimal place, the probability is 0.083.