1 Answer

Adam Ayres · Answer 1 · 2023-08-30T11:01:03+0000

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.

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