Question

What is the probability of getting an even number on each one

Answer 1

Given:

Given that four far dice are thrown.

Required: Probability of getting an even number on each one.

Explanation:

The sample space is

`S=\lbrace(x,y,z,w):\text{ x,y,z,w =1,2,3,4,5,6\textbraceright}`

The number of elements in the sample space is

`\begin{gathered} n(S)=6*6*6*6 \\ =6^4 \end{gathered}`

Let E be the event of getting even on each dice. Then

`E=\lbrace(x,y,z,w);x,y,z,w=2,4,6\rbrace`

The number of elements in E is

`\begin{gathered} n(E)=3*3*3*3 \\ =3^4 \end{gathered}`

The probability of getting even on each dice is

`\begin{gathered} P(E)=(n(E))/(n(S)) \\ =(3^4)/(6^4) \\ =(3^4)/(2^4\cdot3^4) \\ =(1)/(2^4) \\ =(1)/(16) \end{gathered}`

The second option is correct.

Final Answer: The probability of getting even on each dice is 1/16.