Venn Diagrams |

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Notes

Notes for Conditional Probabilities

Practice Problems

For problems 1-9, use the Venn diagram below.

Venn Diagram for Questions 1-4

\(\textbf{1)}\) P (red)
Show Answer
The answer is P (red) \(= \frac{65}{150}=\frac{13}{30}\approx 43.3\)%

\(\textbf{2)}\) P (not red)
Show Answer
The answer is P (not red) \(= \frac{85}{150}=\frac{17}{30}\approx 56.7\)%

\(\textbf{3)}\) P (red and truck)
Show Answer
The answer is P (red and truck) \(= \frac{20}{150}=\frac{2}{15}\approx 13.3\)%

\(\textbf{4)}\) P (red or truck)
Show Answer
The answer is P (red or truck) \(= \frac{125}{150}=\frac{5}{6}\approx 83.3\)%

Venn Diagram for Questions 5-9

\(\textbf{5)}\) P (red | truck)
Show Answer
The answer is P (red | truck) \(= \frac{20}{80}=\frac{1}{4}= 25\)%

\(\textbf{6)}\) P (truck | red)
Show Answer
The answer is P (truck | red) \(= \frac{20}{65}=\frac{4}{13}\approx 30.8\)%

\(\textbf{7)}\) P (red and not truck)
Show Answer
The answer is P (red and not truck) \(= \frac{45}{150}=\frac{9}{30}=30\)%

\(\textbf{8)}\) Are “red” and “truck” independent?
Show Answer
Not independent

\(\textbf{9)}\) Are “red” and “truck” mutually exclusive?
Show Answer
Not mutually exclusive

For problems 10-18, use the Venn diagram below.

Venn Diagram for Questions 10-13

\(\textbf{10)}\) P (fruit)
Show Answer
P (fruit) \(= \frac{32}{100}=32\)%

\(\textbf{11)}\) P (not fruit)
Show Answer
P (not fruit) \(=1- \frac{32}{100}=68\)%

\(\textbf{12)}\) P (fruit and vegetable)
Show Answer
P (fruit and vegetable) \(= \frac{0}{100}=0\)%

\(\textbf{13)}\) P (fruit or vegetable)
Show Answer
P (fruit or vegetable) \(= \frac{32}{100}+\frac{44}{100}=76\)%

Venn Diagram for Questions 14-18

\(\textbf{14)}\) P (fruit | vegetable)
Show Answer
P (fruit | vegetable) \(=0\)%

\(\textbf{15)}\) P (vegetable | fruit)
Show Answer
P (vegetable | fruit) \(=0\)%

\(\textbf{16)}\) P (fruit and not vegetable)
Show Answer
P (fruit and not vegetable) \(= \frac{32}{100}=32\)%

\(\textbf{17)}\) Are “fruit” and “vegetable” independent?
Show Answer
Not independent

\(\textbf{18)}\) Are “fruit” and “vegetable” mutually exclusive?
Show Answer
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?
Show Answer
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?
Show Answer
The answer is \(50 \) shirts

See Related Pages\(\)

\(\bullet\text{ Statistics Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)

\(\bullet\text{ Conditional Probabilites}\)
\(\,\,\,\,\,\,\,\,P(A|B)=\displaystyle\frac{P(A \cap B}{P(B)}…\)

\(\bullet\text{ Independent Events}\)
\(\,\,\,\,\,\,\,\,P(A \cap B)=P(A)P(B)…\)

\(\bullet\text{ Mutually Exclusive Events}\)
\(\,\,\,\,\,\,\,\,P(A \cap B)=0…\)

\(\bullet\text{ Tree Diagrams}\)
\(\,\,\,\,\,\,\,\,\)…

\(\bullet\text{ Two-Way Tables}\)
\(\,\,\,\,\,\,\,\,\)…

\(\bullet\text{ Andymath Homepage}\)

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Notes

Practice Problems

For problems 1-9, use the Venn diagram below.

\(\textbf{1)}\) P (red) Show Answer The answer is P (red) \(= \frac{65}{150}=\frac{13}{30}\approx 43.3\)%

\(\textbf{2)}\) P (not red) Show Answer The answer is P (not red) \(= \frac{85}{150}=\frac{17}{30}\approx 56.7\)%

\(\textbf{3)}\) P (red and truck) Show Answer The answer is P (red and truck) \(= \frac{20}{150}=\frac{2}{15}\approx 13.3\)%

\(\textbf{4)}\) P (red or truck) Show Answer The answer is P (red or truck) \(= \frac{125}{150}=\frac{5}{6}\approx 83.3\)%

\(\textbf{5)}\) P (red | truck) Show Answer The answer is P (red | truck) \(= \frac{20}{80}=\frac{1}{4}= 25\)%

\(\textbf{6)}\) P (truck | red) Show Answer The answer is P (truck | red) \(= \frac{20}{65}=\frac{4}{13}\approx 30.8\)%

\(\textbf{7)}\) P (red and not truck) Show Answer The answer is P (red and not truck) \(= \frac{45}{150}=\frac{9}{30}=30\)%

\(\textbf{8)}\) Are “red” and “truck” independent?Show Answer Not independent

\(\textbf{9)}\) Are “red” and “truck” mutually exclusive?Show Answer Not mutually exclusive

For problems 10-18, use the Venn diagram below.

\(\textbf{10)}\) P (fruit) Show Answer P (fruit) \(= \frac{32}{100}=32\)%

\(\textbf{11)}\) P (not fruit) Show Answer P (not fruit) \(=1- \frac{32}{100}=68\)%

\(\textbf{12)}\) P (fruit and vegetable) Show Answer P (fruit and vegetable) \(= \frac{0}{100}=0\)%

\(\textbf{13)}\) P (fruit or vegetable) Show Answer P (fruit or vegetable) \(= \frac{32}{100}+\frac{44}{100}=76\)%

\(\textbf{14)}\) P (fruit | vegetable) Show Answer P (fruit | vegetable) \(=0\)%

\(\textbf{15)}\) P (vegetable | fruit) Show Answer P (vegetable | fruit) \(=0\)%

\(\textbf{16)}\) P (fruit and not vegetable) Show Answer P (fruit and not vegetable) \(= \frac{32}{100}=32\)%

\(\textbf{17)}\) Are “fruit” and “vegetable” independent?Show Answer Not independent

\(\textbf{18)}\) Are “fruit” and “vegetable” mutually exclusive?Show Answer 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? Show Answer 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? Show Answer The answer is \(50 \) shirts