Notes
Practice Problems
For problems 1-9, use the Venn diagram below.
\(\textbf{1)}\) P (fruit)
P (fruit) \(= \frac{32}{100}=32\)%
\(\textbf{2)}\) P (not fruit)
P (not fruit) \(=1- \frac{32}{100}=68\)%
\(\textbf{3)}\) P (fruit and vegetable)
P (fruit and vegetable) \(= \frac{0}{100}=0\)%
\(\textbf{4)}\) P (fruit or vegetable)
P (fruit or vegetable) \(= \frac{32}{100}+\frac{44}{100}=76\)%
\(\textbf{5)}\) P (fruit | vegetable)
P (fruit | vegetable) \(=0\)%
\(\textbf{6)}\) P (vegetable | fruit)
P (vegetable | fruit) \(=0\)%
\(\textbf{7)}\) P (fruit and not vegetable)
P (fruit and not vegetable) \(= \frac{32}{100}=32\)%
\(\textbf{8)}\) Are “fruit” and “vegetable” independent?
Not independent
\(\textbf{9)}\) Are “fruit” and “vegetable” mutually exclusive?
Yes, they are mutually exclusive.
\(\textbf{10)}\) Are “red” and “truck” mutually exclusive?
No, they are not mutually exclusive.
See Related Pages\(\)
In Summary
Mutually exclusive events (aka disjoint events) are events that cannot occur at the same time. A lot of interesting probabilities come from recognizing if 2 events are mutually exclusive.
\(P\left(A \text{ or } B\right) = P\left(A\right) + P\left(B\right)\)
\(P\left(A \text{ and } B\right) = 0 \)
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