Lab Rat Independence

A scientist is conducting an experiment with two rats, and she noted the incidence of the following events each day.

\(A=\text{The 1st rat receives an extra food pellet for the day}\)

\(B=\text{The 1st rat runs in the exercise wheel that day}\)

\(C=\text{The 2nd rat runs in the exercise wheel that day}\)

Over the course of the experiment, the scientist recorded the following probabilities:

\(\begin{array}{111} P(A)=0.5 & P(B)=0.2 & P(C)=0.1 \\ P(A\cap B)=0.1 & P(A\cap C)=0.05 & P(B\cap C)=0.02 \\ P(A\cap B\cap C)=0.01 \\ \end{array}\)

Are the events mutually independent?

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