Probability 1 – Theoretical Probability SAMs 1 Maths Unit 1 Q5 5. In a game, cards are chosen at random from two boxes. Box A contains these two cards

. Box B contains these five cards

. One card is chosen at random from box A and one card is chosen at random from box B. The two numbers on the chosen cards are multiplied together to give a score. The person choosing the cards wins a prize if the score is more than zero. Complete the table below to show all the possible scores and calculate an estimate for the number of prize winners when 70 play the game once. [6]

Box B

SAMs 1 Maths Unit 1 Q10 10. Mair either walks, cycles, travels by car or travels by bus to work each day. Her method of travel each day is independent of her method of travel on any other day.

BOX A

The table below shows the probability for three of her methods of travel on any randomly chosen day. Method of Transport

Walk Bike Car Bus

Probability 0.45 0.1 0.25

(a) Calculate the probability that, on any randomly chosen day, she walks to work. [2] ..………………………………………………………………………………………………… ..………………………………………………………………………………………………… (b) What is the probability that, on any randomly chosen day, she either travelled to work by car or by bus? [2] ..………………………………………………………………………………………………… ..………………………………………………………………………………………………… (c) What is the probability that, in any randomly chosen week, Mair travelled to work by car on the Monday and by bus on the Tuesday? [2] ..………………………………………………………………………………………………… ..………………………………………………………………………………………………… SAMs 1 Maths Unit 2 Q14 14. Carys has a Monday to Friday job and a weekend job. Working Monday to Friday and working weekends are independent events. In any given week, the probability that Carys works every day from Monday to Friday is 0·65. The probability that she works both days during a weekend is 0·2. (a)Complete the following tree diagram. [2]

(b) Calculate the probability that next week Carys will work every day from Monday to Sunday. [2] ..………………………………………………………………………………………………… ..………………………………………………………………………………………………… SAMs 2 Maths Unit 1 Q3 3. Sian states

‘When a fair coin is tossed and a fair dice is thrown, the probability of

getting a head and an even number is ½’ Is Sian correct? You must show enough working to justify your answer. [4] ………………………………………………………………………………………………………………………………………………………

Works every day from Monday to Friday.

Works both days during a weekend.

YES

YES

YES

No

No

No

SAMs 2 Maths Unit 1 Q9. 9. At lunchtime on any given day, Alun has one of the following drinks: coffee, tea, mineral water or fruit juice. His choice of drink each day is independent of his choice of drink on any other day. The table below shows the probabilities for three of his choices of drink on any randomly chosen day.

(a) Calculate the probability that, on any randomly chosen day, Alun has a fruit juice at lunchtime. [2] ..………………………………………………………………………………………………… ..………………………………………………………………………………………………… (b) What is the probability that, on any randomly chosen day, he has either tea or mineral water at lunchtime? [2] ..………………………………………………………………………………………………… ..………………………………………………………………………………………………… (c) What is the probability that, in any randomly chosen week, Alun has coffee on the Tuesday and has tea on the Friday? [2] ………………………………………………………………………………………………… ..………………………………………………………………………………………………… SAMs 2 Maths Unit 1 Q15. 15. For a particular visitor to Gwynedd, taking a trip up Snowdon is independent of visiting Caernarfon Castle. The probability that the visitor takes a trip up Snowdon and visits Caernarfon Castle is 0·12. (a) Complete the following tree diagram. [4]

(b) Calculate the probability that the visitor does not go up Snowdon and does not visit Caernarfon Castle. [2] ……………………………………………………………………………………………… SAMs 2 Maths Unit 2 Q3 3. a) Circle the correct answer for each of the following statements. i) Helen has bought one of the eighty tickets sold in a raffle. The probability that Helen wins the top prize in the raffle is [1]

ii) One ball is selected at random from a box containing 5 blue balls, 4 red balls and 1 yellow ball. The probability that the selected ball is blue is [1]

b) A bag contains some red, green and black beads. One bead is selected at random from the bag. The probability of selecting a green bead form the bag is 1/3. Which of the following sets of beads could have been in the bag? Circle your answer. [1]

2 red 1 green 1 black

3 red 6 green 3 black

3 red 3 green 4 black

7 red 4 green 1 black

5 red 3 green 4 black

WJEC Nov 2016 Maths Unit 1 Q5 5. Three red cards have the following numbers written on them.

Four green cards have the following numbers written on them.

In a game, the cards are turned face down. A player chooses one red card and one green card at random. The player’s score is the sum of the two numbers.

a) Complete the following table. [1]

b) A player wins a prize if the score is more than 9.

Safira plays the game once. What is the probability that she wins a prize? [2]

…………………………………………………………………………………………………………………………….

c) 60 people play the game once. Approximately how many people would you expect to win a prize? [2]

…………………………………………………………………………………………………………………………….

WJEC Nov 2016 Maths Unit 1 Q12

WJEC Nov 2016 Maths Unit 1 Q16

WJEC Summer Maths 2017 Unit 1 Q4

WJEC Summer Maths 2017 Unit 1 Q6

WJEC Summer Maths 2017 Unit 1 Q10

WJEC Maths Summer 2017 Unit 2 Q17

Source unknown

a) There are 50 members in a tennis club. Some of these members have visited the Wimbledon Championship and some have not.

This information is displayed in the following table. Male Female Total Visited Wimbledon Championship

24 5 29

Have not visited Wimbledon Championship

6 15 21

Total 30 20 50 What is the probability that a member chosen at random

i) Is male? [1] ……………………………………………………………….

ii) Has visited the Wimbledon Championship? [1] ……………………………………………………………….

iii) Is a female who has not visited the Wimbledon Championship? [1] ……………………………………………………………….

WJEC MIM Unit 1 June 15 Q11 11. a) Place the whole numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 in the correct positions in the Venn diagram. [3]

b) A whole number is selected at random from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Odd numbers Multiples of 5

Factors of 24

Find the probability that the number selected is: An odd number …………………

An odd number that is a factor of 24 …………………. Not a multiple of 5 and not a factor of 24 .………………… [3]

WJEC MIM Unit 1 June 15 Q12 12. A spinner shows 5 colours. The spinner was spun 50 times. Some of the outcomes were recorded in a table. Colour Purple Black White Red Yellow

Number of times

7

8

20

……..

……..

a) Red occurred twice as many times as yellow. Complete the table above [1] ………………………………………………………………………………………..

b) Write down the best estimate for the following probabilities on a single spin. You must express each of your answers as a decimal. i) The probability of obtaining black [1]

……………………………………………………………………………

ii) The probability of not obtaining white [2] ……………………………………………………………………………

WJEC MIM Unit 1 June 14 Q10 10 a) A bag contains only red, yellow, green and blue coloured sweets. The table below shows the probability of choosing each colour of sweet, when one sweet is chosen at random from the bag. Colour Red Yellow Green Blue

Probability 0.2 0.15 0.25

i) What is the probability of choosing a blue sweet? [2]

……………………………………………………………………

ii) Which two colours are least likely to be chosen? [1] ……………………………………………………………………

b)For a different bag of sweets, the probability of choosing a purple sweet is 0.7 What is the probability of not choosing a purple sweet? [2] ……………………………………………………………………

WJEC MIM Unit 1 Jan 14 Q12 12. A fair dice and a fair coin are thrown once. a) Fill in the table below to show all the possible outcomes. [2] 1 2 3 4 5 6

Head (H) H1 H2

Tail (T) TI

b) Write down the probability of obtaining a head and a 4 [1] ……………………………………………………………………… c) Write down the probability of obtaining a tail and a number less than 3. [1] ………………………………………………………………………