10 questions · 41 marks · ≈ 41 min
Dora has the following number cards.
She takes a card at random, replaces the card and then takes a second card. She adds the numbers on the two cards she has taken and records the total.
Complete the following table to show all of her possible totals.
| First card | ||||||
|---|---|---|---|---|---|---|
| Second card | Total | 2 | 2 | 3 | 5 | 6 |
| 2 | 4 | 4 | 5 | 7 | 8 | |
| 2 | 4 | 4 | 5 | 8 | ||
| 3 | 5 | 5 | 8 | 9 | ||
| 5 | 7 | 8 | 10 | 11 | ||
| 6 | 8 | 8 | 9 | 11 | 12 |
Find the probability that her total is
i) an even number,
(2 marks)
ii) a multiple of 3 or 4.
(2 marks)
A and B are two events.
Some probabilities are shown on the Venn diagram.
Work out
Geoff has two fair spinners.
He spins both spinners and multiplies the numbers on each spinner.
Complete the table.
| Spinner B | Spinner A | ||
|---|---|---|---|
| x | 1 | 7 | 9 |
| 2 | 2 | 14 | 18 |
| 3 | 3 | 21 | 27 |
| 4 | 4 | 28 | |
| 5 | 5 | 35 |
Geoff wants to work out the probability that the outcome of the multiplication is an even number or a prime number. Here is his working.
| The probability the outcome is an even number is The probability the outcome is a prime number is The probability the outcome is an even number or a prime number is |
|---|
Geoff is wrong. Explain his error and give the correct answer.
In a survey, 60 students were asked whether they have a bank account (B) and whether they have a part-time job (J).
The number of students who had neither a bank account nor a part-time job was x.
The Venn diagram shows the results in terms of x.
One of the 60 students is chosen at random. Find the probability that they have a bank account. Show your working.
This is a fair 5-sided spinner.
Ciara spins the spinner twice and records the product of the two scores.
i) Complete the table.
| Second spin | First spin | ||||
|---|---|---|---|---|---|
| x | 1 | 2 | 2 | 3 | 4 |
| 1 | 1 | ||||
| 2 | 4 | ||||
| 2 | |||||
| 3 | |||||
| 4 | 12 |
(2 marks)
ii) Find the probability that the product is a multiple of 3.
(2 marks)
xi = { 2 , 4 , 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 , 26 , 28 , 30 } A = { Multiples of 3 } B = { Factors of 12 }
Complete the Venn diagram to show this information.
Write down the probability of
calligraphic E = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } A = { 1 , 5 , 6 , 8 , 9 } B = { 2 , 6 , 9 }
Complete the Venn diagram to represent this information.
A number is chosen at random from the universal set .
Find the probability that the number is in the set .
In a survey of 50 people,
30 owned a cat
25 owned a dog
6 owned neither a cat or a dog
Complete the Venn diagram to show this information.
One person is chosen at random.
Find the probability that the person owns a cat and a dog.
Here is some information about 80 people who play in bands.
12 are singers but not guitar players. 30% are neither a singer nor a guitar player. of the guitar players are also singers.
Complete this Venn diagram to represent the information.
ξ = 80 people who play in bands S = singers G = guitar players
Kaiyo has two fair dice. Kaiyo rolls each die once. Kaiyo adds together the number to get a total score.
Complete the table to show all possible scores.
| + | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | ||||||
| 2 | ||||||
| 3 | ||||||
| 4 | ||||||
| 5 | ||||||
| 6 |
Find the probability that
(i) Kaiyo’s total score is 4
(ii) Kaiyo’s total score is more than 9