Notes
Practice Problems
For problems 1-9, use the Venn diagram below.
\(\textbf{1)}\) P (red)
The answer is P (red) \(= \frac{65}{150}=\frac{13}{30}\approx 43.3\)%
![Link to Youtube Video Solving Question Number 1](https://andymath.com/wp-content/uploads/2020/08/play-video.jpg")
\(\textbf{2)}\) P (not red)
The answer is P (not red) \(= \frac{85}{150}=\frac{17}{30}\approx 56.7\)%
\(\textbf{3)}\) P (red and truck)
The answer is P (red and truck) \(= \frac{20}{150}=\frac{2}{15}\approx 13.3\)%
\(\textbf{4)}\) P (red or truck)
The answer is P (red or truck) \(= \frac{125}{150}=\frac{5}{6}\approx 83.3\)%
\(\textbf{5)}\) P (red | truck)
The answer is P (red | truck) \(= \frac{20}{80}=\frac{1}{4}= 25\)%
\(\textbf{6)}\) P (truck | red)
The answer is P (truck | red) \(= \frac{20}{65}=\frac{4}{13}\approx 30.8\)%
\(\textbf{7)}\) P (red and not truck)
The answer is P (red and not truck) \(= \frac{45}{150}=\frac{9}{30}=30\)%
\(\textbf{8)}\) Are “red” and “truck” independent?
Not independent
\(\textbf{9)}\) Are “red” and “truck” mutually exclusive?
Not mutually exclusive
For problems 10-18, use the Venn diagram below.
\(\textbf{10)}\) P (fruit)
P (fruit) \(= \frac{32}{100}=32\)%
\(\textbf{11)}\) P (not fruit)
P (not fruit) \(=1- \frac{32}{100}=68\)%
\(\textbf{12)}\) P (fruit and vegetable)
P (fruit and vegetable) \(= \frac{0}{100}=0\)%
\(\textbf{13)}\) P (fruit or vegetable)
P (fruit or vegetable) \(= \frac{32}{100}+\frac{44}{100}=76\)%
\(\textbf{14)}\) P (fruit | vegetable)
P (fruit | vegetable) \(=0\)%
\(\textbf{15)}\) P (vegetable | fruit)
P (vegetable | fruit) \(=0\)%
\(\textbf{16)}\) P (fruit and not vegetable)
P (fruit and not vegetable) \(= \frac{32}{100}=32\)%
\(\textbf{17)}\) Are “fruit” and “vegetable” independent?
Not independent
\(\textbf{18)}\) Are “fruit” and “vegetable” mutually exclusive?
Yes, they are mutually exclusive.
\(\textbf{19)}\) At a shop there are 40 red shirts, and 50 medium sized shirts. There are 60 shirts that are either red, medium or both. How many medium sized red shirts are there?
The answer is \(30 \) shirts
\(\textbf{20)}\) There are 200 shirts in a shop. 45% are red. 60% are medium. 30% are red and medium. How many shirts are neither red nor medium in size?
The answer is \(50 \) shirts
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