Answered

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An experiment consists of rolling a standard six-sided die once.

An Experiment Consists Of Rolling A Standard Sixsided Die Once class=

Sagot :

Two events are independent if

[tex]P(A)\cdot P(B)=P(B\cap A)[/tex]

Or

[tex]\begin{gathered} P(B)=\frac{P(B\cap A)}{P(A)} \\ P(B)=P(B|A) \end{gathered}[/tex]

Event A is "rolling a 5":

[tex]P(A)=\frac{1}{6}[/tex][tex]P(B\cap A)=\frac{1}{6}[/tex]

Event B is "rolling an odd number":

Odd number are 1, 3 and 5

[tex]P(B)=\frac{3}{6}=\frac{1}{2}[/tex]

Then, substitute

[tex]\begin{gathered} P(B)=\frac{P(B\cap A)}{P(A)} \\ P(A)=\frac{P(B\cap A)}{P(B)}=\frac{\frac{1}{6}}{\frac{1}{2}}=\frac{1}{3} \end{gathered}[/tex]

This is:

[tex]\begin{gathered} P(B)\ne\frac{P(B\cap A)}{P(A)} \\ therefore \\ P(B)\ne P(B|A) \end{gathered}[/tex]

which makes the events dependent.

Answer: D.

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