10.05 Mutually exclusive events

A random card is picked from a standard deck. Find the probability that the card is:

A fair die is rolled. Find the probability of rolling:

A random card is picked from a standard deck. Find the probability that the card is:

For the following Venn diagrams:

a

b

For each of the following groups of probabilities:

Two events A and B are mutually exclusive. If P \left( A \right) =0.37 and P \left( A \text{ or } B \right)=0.73, find P \left(B \right).

If A and B are mutually exclusive and P \left( A \right) = \dfrac{1}{4} and P \left( B \right) = \dfrac{1}{2}, find P \left( A \cup B \right).

In an experiment, a die is rolled and the number appearing on the uppermost face is noted. Describe P(A \cup B) if:

• Event A = getting an odd number

• Event B = getting a multiple of 3

If P \left( A \right) = \dfrac{1}{5}, P \left( B \right) = \dfrac{1}{6} and P \left( A \cap B \right) = \dfrac{1}{30}, find P \left ( A \cup B \right).

If P \left( A \right) = \dfrac{1}{3}, P \left( B \right) = \dfrac{1}{5} and P \left( A \cup B \right) = \dfrac{2}{15}, find P \left( A\cap B \right).

If P \left( A \cup B \right) = \dfrac{7}{15}, P \left( A \cap B \right) = \dfrac{1}{15} and P \left( A \right) = \dfrac{1}{3}, find P \left( B \right).

If P \left( A \right) =0.8, P \left( B \right)=0.75 and P \left( A \text{ and } B \right)=0.6, find P \left( A \text{ or } B \right).

In a particular high school where there are 91 year 12 students, 40 students study Extension 2 English and 36 students study Extension 2 Mathematics. The Venn diagram depicts this:

If a student is randomly chosen, find the probability that this student is studying:

The Venn diagram shows the number of students in a school playing Rugby League, Rugby Union, both or neither:

The Venn diagram shows the decisions of 448 workers to either work or strike on a particular day of industrial action.

Find the probability that a worker selected randomly chose to:

a

Strike

b

Strike and work.

c

Work and not strike.

d

Work or strike.

e

Neither work nor strike.

The Venn diagram shows the decisions of 535 consumers choosing to buy an iPhone and consumers choosing to buy a Blackberry:

If a consumer is selected at random, find the probability that he chose to buy:

The Venn diagram depicts the investment choices of 1232 investors:

Find the probability that an investor randomly selected has investments in:

A florist collected a sample of her flowers and divided them into the appropriate categories as shown in the Venn diagram:

Find the probability that a flower is:

Some people were asked what form of exercise they do. The results are displayed in the Venn diagram below:

a

State whether the following are correct:

i

12 people walk only.

ii

22 people run only.

iii

6 people run only.

iv

6 people walk only.

b

If one person is chosen at random, find the probability that they walk for exercise.

In an experiment, a number is chosen randomly from the numbers listed below:

\left \{2, 3, 5, 6, 7, 10, 12, 14, 15, 16, 19, 20 \right \}

Out of 23 school kids, 12 play basketball and 13 play football, whilst 5 play both sports.

a

For the given Venn diagram, find the value of:

i

A

ii

B

iii

C

iv

D

b

Find the probability that a student plays football or basketball, but not both.

c

Find the probability that a student plays both football and basketball.

In a music school of 129 students, 83 students play the piano, 80 students play the guitar and 14 students play neither.

In a survey, 59 students were asked to select all the subjects they enjoyed out of Maths , English and Science.

In a survey of 31 students, it was found that:

Among a group of 63 students, 12 students are studying philosophy, 48 students are studying science, and 7 students are studying neither subject.

Among a group of students studying economics and/or law, a single student is randomly chosen, and the probabilities are as follows:

• P \left( \text{studies economics} \right) = 0.5

• P \left( \text{studies neither} \right) = 0

• P \left( \text{studies law} \right) = 0.7

Find the probability that a student chosen at random studies both economics and law.

The employees of Squiggle were discussing where they should hold their end of year party. Of all of the employees:

• 51 would not go to a restaurant

• 58 would not go to a bowling alley

• 57 would not go to a theme park

• 22 would go to neither a restaurant nor a bowling alley

• 25 would go to neither a bowling alley nor the theme park

• 23 would go to neither a restaurant nor the theme park

• 4 would not go to a restaurant or a bowling alley or to the theme park

• 6 would go to all three places.

How many people in total work at Squiggle?