SL Probability

Draw a Venn diagram from this information to use for questions 1 - 7.

In a class of 30 students, 18 have a dog, 20 have a cat and 3 have neither.

How many students have both a cat and a dog?

• 11

• 10

• 9

• 8

If a student is chosen at random, what is the probability that they own a cat but not a dog?

• $\frac{3}{10}$

• $\frac{1}{3}$

• $\frac{2}{3}$

• $\frac{11}{30}$

If a student is chosen at random, what is the probability they own exactly one pet?

• $\frac{8}{15}$

• $\frac{27}{30}$

• $\frac{11}{30}$

• $\frac{3}{5}$

If a student is chosen at random, what is the probability that they own a cat, given that they own a dog?

• $\frac{11}{18}$

• $\frac{11}{20}$

• $\frac{7}{18}$

• $\frac{9}{20}$

If 2 students are chosen at random, what is the probability they both own dogs?

• $\frac{51}{145}$

• $\frac{9}{25}$

• $\frac{54}{145}$

• $\frac{17}{50}$

Are the events A - "owning a cat" and B = "owning a dog" independent?

• No because $P\left(A\right)\times P\left(B\right)\ne P\left(A\cap B\right)$

• Yes because $P\left(A\right)\times P\left(B\right)=P\left(A\cap B\right)$

• No because $P\left(A\right)\times P\left(B\right)\ne P\left(A\cup B\right)$

• Yes because $P\left(A\right)\times P\left(B\right)=P\left(A\cup B\right)$

Are the events A - "owning a cat" and B = "owning a dog" mutually exclusive?

• No because $P\left(A\cap B\right)\ne0$

• No because $P\left(A\cup B\right)\ne0$

• Yes because you can own both.

• No because you can other types of pets too.

Create a Venn Diagram and use it for questions 8 - 10.

For events C and D it is known that:

 $P\left(C\right)=0.7$  ;  $P\left(C'\cap D'\right)=0.25$  ;  $P\left(D\right)=0.2$  
Find  $P\left(C\cap D'\right)$  

• 0.55

• 0.45

• 0.5

• 0.6

 $Find\ P\left(D\left|C\right|\right)$  

•  $\frac{3}{14}$  

•  $\frac{3}{4}$  

•  $\frac{1}{4}$  

•  $\frac{11}{14}$  

 $Find\ P\left(C\cup D'\right)$  

• 0.95

• 0

• 0.55

• 0.8