Question

find the probability for each situation. question 1. A number cube is a spun two times. find the probability that it will land on a event number both times.

Answer 1

In a number cube, the sample space is {1,2,3,4,5,6}.

The even numbers are {2,4,6}.

Determine the probability for cube landing with even number first times.

`\begin{gathered} P(A)=(3)/(6) \\ =(1)/(2) \end{gathered}`

Determine the probability for cube landing with even number in second time.

`\begin{gathered} P(B)=(3)/(6) \\ =(1)/(2) \end{gathered}`

Since both rolling of dices are independent to each other. So probability for getting even number on both time is,

`\begin{gathered} P(AandB)=P(A)\cdot P(B) \\ =(1)/(2)\cdot(1)/(2) \\ =(1)/(4) \end{gathered}`

Answer: 1/4