When picking a random card from a standard pack, which two of the four events listed share no common outcomes?
Event A: picking a black card
Event B: picking a King
Event C: picking a spade
Event D: picking a club
A random card is picked from a standard deck. Find the probability that the card is:
A spade or diamond
A king or a \rq 3 \rq
An ace of spades or a king of hearts
A fair die is rolled. Find the probability of rolling:
A factor of 9 or an even number
A number that is even and prime
A random card is picked from a standard deck. Find the probability that the card is:
Red or a diamond
An ace or a diamond
An ace of spades or an ace of clubs
A black or a face card
For the following Venn diagrams:
Calculate the value of x.
State whether the events A and B are mutually exclusive.
For each of the following groups of probabilities:
Find P \left( A \cap B \rq \right).
Find P \left( B \cap A \rq \right).
Hence, find P \left( A \cap B \right).
State whether the events A and B are mutually exclusive.
P \left( A \cup B \right) = 0.6, P \left( A' \right) = 0.6 and P \left( B' \right) = 0.7
P \left( A \cup B \right) = 0.3, P \left( A' \right) = 0.8 and P \left( B' \right) = 0.9
P \left( A' \cap B' \right) = 0.1, P \left( A \right) = 0.8 and P \left( B \right) = 0.3
P \left( A' \cap B' \right) = 0.2, P \left( A \right) = 0.1 and P \left( B \right) = 0.7
The Venn diagram shows the party preferences of voters in a sample of the population.
Find the probability that a random voter has a preference for both Labour and Liberal.
Are the preferences of voters in this population mutually exclusive?
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:
Extension 2 English and Extension 2 Mathematics.
Extension 2 English only.
Extension 2 Mathematics only.
Extension 2 Mathematics or Extension 2 English.
Neither subject.
The Venn diagram shows the results of a survey identifying what colours a group of children liked:
Find the probability of a child liking:
Green and pink.
Green or pink but not both.
Consider the Venn diagram:
Find:
P\left( A \right)
P \left( B \right)
P \left( \text{not } A \right)
P \left( \text{not } B \right)
The Venn diagram shows the number of students in a school playing Rugby League, Rugby Union, both or neither:
How many students play both Rugby League and Rugby Union?
How many students play at least one of the two sports?
How many students play neither Rugby League nor Rugby Union?
How many students are there altogether?
Find the probability that a student chosen randomly plays both Rugby League and Rugby Union.
Find the probability that a student chosen randomly plays Rugby League or Rugby Union or both.
The Venn diagram shows the number of students choosing to study on the night before an exam, and the number of students choosing to party:
Find the number of students that chose:
To party
Not to study
Neither to study nor party
Find the probability that a student chosen at random chose:
Not to party
To study and party
To study only
To study or party
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:
Strike
Strike and work.
Work and not strike.
Work or 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:
A Blackberry.
A Blackberry only.
Both phones.
An iPhone or a Blackberry.
Neither phones.
An iPhone but not a Blackberry.
The Venn diagram depicts the investment choices of 1232 investors:
Find the probability that an investor randomly selected has investments in:
Bonds
Bonds and real estate.
Bonds or real estate.
Bonds and real estate but not shares.
Shares, bonds and real estate.
Real estate and shares but not bonds.
Shares, bonds or real estate.
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:
Not red but has thorns.
Not red and does not have thorns.
Some people were asked what form of exercise they do. The results are displayed in the Venn diagram below:
State whether the following are correct:
12 people walk only.
22 people run only.
6 people run only.
6 people walk only.
If one person is chosen at random, find the probability that they walk for exercise.
Consider the given Venn diagram:
Find:
P \left( A \text{ but not } B \right)
P \left( A \text{ and } B \right)
P \left( A \text{ or } B \right)
P \left( \text{ neither } A \text{ nor } B \right)
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 \}
Event A: odd number is chosen
Event B: multiple of 4 is chosen
Which of the following has the largest probability?
Find:
P \left( A \cap B \right)
P\left( \left(A \cap B \right)' \right)
P \left( A' \cap B' \right)
P \left( A' \cup B \right)
A group of people were randomly selected and asked which modes of transport they used to get to work. The Venn diagram shows the results:
If one of them is chosen at random, the probability that they catch a bus is \dfrac{12}{58}. How many people said they catch a bus and a train?
Out of 23 school kids, 12 play basketball and 13 play football, whilst 5 play both sports.
For the given Venn diagram, find the value of:
A
B
C
D
Find the probability that a student plays football or basketball, but not both.
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.
Construct a Venn diagram for this situation.
Find the probability that a student chosen at random plays:
Both the piano and the guitar
The piano or the guitar
Neither the piano nor the guitar
In a survey, 59 students were asked to select all the subjects they enjoyed out of Maths , English and Science.
Construct a Venn diagram for this situation.
Find the probability that a student likes both Maths and only one other subject.
Find the probability that a student likes only one of the subjects.
In a survey of 31 students, it was found that:
Construct a Venn diagram for this situation.
Find the probability that a randomly selected student plays all three sports.
Among a group of 63 students, 12 students are studying philosophy, 48 students are studying science, and 7 students are studying neither subject.
How many students are studying philosophy and science?
If a student is picked at random, find the probability that they study at least one of these subjects.
Find the probability that a randomly selected student studies only one of the subjects.
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?