Ben has 3 shirts, each in a different colour: crimson (C), pink (P) and white (W), and 4 ties, each in a different colour: blue (B), grey (G), red (R) and yellow (Y).
How many different combinations are possible?
Find the probability that he is wearing:
A pink shirt and yellow tie.
A pink shirt.
A pink or white shirt.
| C | P | W | |
|---|---|---|---|
| B | C,B | P,B | W,B |
| G | C,G | P,G | G,W |
| R | C,R | P,R | W,R |
| Y | C,Y | P,Y | W,Y |
A player rolls two dice and finds the sum of the numbers on the faces.
List the sample space for the sum of two dice.
Find the probability the dice will sum to five.
Find the probability the dice will sum to an odd number.
| 1 | 2 | 3 | 4 | 5 | 6 | |
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 |
A player rolls two dice and finds the difference, that is, the largest number minus the smaller number.
List the sample space for the difference of two dice.
Find the probability the dice will have a difference of zero.
Find the probability the dice will have a difference of five.
| 1 | 2 | 3 | 4 | 5 | 6 | |
|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 2 | 3 | 4 | 5 |
| 2 | 1 | 0 | 1 | 2 | 3 | 4 |
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| 4 | 3 | 2 | 1 | 0 | 1 | 2 |
| 5 | 4 | 3 | 2 | 1 | 0 | 1 |
| 6 | 5 | 4 | 3 | 2 | 1 | 0 |
Twenty-two balls coloured either green or black and numbered 1 to 11 are placed in a bag. The table shows all the possible outcomes that can occur:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Green | \text{G}1 | \text{G}2 | \text{G}3 | \text{G}4 | \text{G}5 | \text{G}6 | \text{G}7 | \text{G}8 | \text{G}9 | \text{G}10 | \text{G}11 |
| Black | \text{B}1 | \text{B}2 | \text{B}3 | \text{B}4 | \text{B}5 | \text{B}6 | \text{B}7 | \text{B}8 | \text{B}9 | \text{B}10 | \text{B}11 |
Find the probability that a ball drawn at random from the bag:
Is black.
Has the number 2.
Has the number 2 or 7.
Has a number 3 or higher.
Is green and has the number 5.
Is green or has the number 5.
In a boardgame a player rolls two six-sided dice but can only move the number of spaces as the largest number rolled. The table shows the possible outcomes:
List the sample space for the largest number rolled.
Find the probability a player can move 4 spaces.
What is the most likely number of spaces a player can move?
Find the probability a player moves an even number of spaces.
Find the probability a player can move 2 or 5 spaces.
| 1 | 2 | 3 | 4 | 5 | 6 | |
|---|---|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 |
| 2 | 2 | 2 | 3 | 4 | 5 | 6 |
| 3 | 3 | 3 | 3 | 4 | 5 | 6 |
| 4 | 4 | 4 | 4 | 4 | 5 | 6 |
| 5 | 5 | 5 | 5 | 5 | 5 | 6 |
| 6 | 6 | 6 | 6 | 6 | 6 | 6 |
Two dice are rolled, and the combination of numbers rolled on the dice is recorded.
Complete the table of outcomes:
| 1 | 2 | 3 | 4 | 5 | 6 | |
|---|---|---|---|---|---|---|
| 1 | 1,1 | 1,2 | ||||
| 2 | 2,1 | |||||
| 3 | ||||||
| 4 | ||||||
| 5 | ||||||
| 6 |
Find the following probabilities for the two numbers rolled:
P(1 and 4)
P(1 then 4)
P(difference =4)
P(product =12)
P(difference \leq 2)
P(difference =3)
P(product =20)
P(difference \leq 1)
If the numbers appearing on the uppermost faces are added, state whether the following are true or false:
A sum greater than 7 and a sum less than 7 are equally likely.
A sum greater than 7 is more likely than a sum less than 7.
A sum of 5 or 9 is more likely than a sum of 4 or 10.
An even sum is more likely than an odd sum.
The following two spinners are spun and the result of each spin is recorded:
Complete the table to represent all possible combinations:
State the total number of possible outcomes.
Find the probability that the spinner lands on a consonant and an even number.
Find the probability that the spinner lands on a vowel or a prime number.
| A | B | C | |
|---|---|---|---|
| 1 | 1,A | ||
| 2 | 2,C | ||
| 3 |
The following spinner is spun and a normal six-sided die is rolled:
| W | X | Y | Z | |
|---|---|---|---|---|
| 1 | 1,W | |||
| 2 | 2,Z | |||
| 3 | ||||
| 4 | ||||
| 5 | 5,X | |||
| 6 |
Complete the table above to represent all possible outcomes.
State the total number of possible outcomes.
Find the probability that the spinner lands on X and the die rolls a 1.
Find the probability that the spinner lands on W and the die rolls an odd number.
Find the probability that the spinner doesn’t land on Z and the die rolls an even number.
A coin is tossed and a die is rolled simultaneously.
Complete the following table to display the possible outcomes:
| 1 | 2 | 3 | 4 | 5 | 6 | |
|---|---|---|---|---|---|---|
| Heads | \text{H,1} | \text{H,3} | \text{H,4} | \text{H,6} | ||
| Tails | \text{T,2} | \text{T,3} | \text{T,5} |
How many possible outcomes are there?
Determine the probability of rolling a 1.
Determine the probability of rolling an even number.
Determine the probability of tossing a head and rolling an even number.
Box A contains 2 red and 2 blue marbles while Box B contains 1 green, 2 yellow and 1 red marbles. A marble is randomly selected from each box.
Complete the given table to represent all possible outcomes:
Determine the probability of:
Drawing marbles the same colour.
Drawing marbles of different colour.
Drawing a red and a yellow marble.
The draw containing at least one red marble.
| G | Y | Y | R | |
|---|---|---|---|---|
| R | R,G | R,Y | R,R | |
| R | R,Y | R,R | ||
| B | B,G | B,Y | B,R | |
| B | B,Y | B,Y |
The following spinner is spun and a normal six-sided die is rolled at the same time. The product of their respective results is recorded.
Construct a table to represent all possible outcomes.
State the total number of possible outcomes.
Find the probability of an odd product.
Find the probability of rolling a 5 on the dice and scoring an even product.
Find the probability of spinning a 3 on the spinner or scoring a product which is a multiple of 4.
The following two spinners are spun and the sum of their results is recorded:
Spinner 1
Spinner 2
Construct a table to represent all possible outcomes.
State the total number of possible outcomes.
Find the probability that the first spinner lands on an even number and the sum is even.
Find the probability that the first spinner lands on a prime number and the sum is odd.
Find the probability that the sum is a multiple of 4.
Two spinners labelled 1 to 4 are spun simultaneously and the results added:
Spinner 1
Spinner 2
Construct a table to represent all possible outcomes.
List the sample space for the sum of the two spinners.
Determine the probability of:
An even result.
A result greater than 6.
A result less than 5 and even.
A result less than 5 or even.
A two-digit number is formed by spinning the following two spinners with Spinner 1 being the first digit and Spinner 2 being the second digit in the number:
Spinner 1
Spinner 2
Construct a table to represent all possible outcomes.
Determine the probability the number formed:
Is 25.
Is even.
Is prime.
Is divisible by 5.
Is divisible by 5 and odd.
Contains at least one 2.