Homework on Co-Ordinates - Foundation

Teacher Assessment The Robert Smyth School Topic 1 Mathematics Faculty Name: Probability HW1 – Grade F/E Innovation & excellence Probability scale and listing outcomes

1. The probabilities of the following events have been marked on the probability scale below.

A: The next person to pass you will be less than 80 years old. B: Tomorrow will be Sunday. C: A fair three-sided spinner, coloured red, blue and green, will land on red.

Label each arrow with a letter to show which event it represents. (2)

2. A fair six-sided dice is thrown once.

The probabilities of the following events have been marked on the probability scale below.

A: An even number is thrown.

B: A ‘7’ is thrown.

C: A number less than 5 is thrown.

Label each arrow with the letter to show which event it represents. (Total 3 marks)

The Robert Smyth School 1 The Robert Smyth School Topic 1 Mathematics Faculty Probability Innovation & excellence

3. There are 10 beads in a bag. Three beads are green, three are red and four are yellow. One bead is taken out of the bag at random.

The probabilities of three events have been marked on the probability scale below.

A: The bead is yellow. B: The bead is white. C: The bead is not red.

Label each arrow with the letter to show which event it represents. (Total 3 marks)

4. A fair spinner has five sections. Two sections are red, one is white, one is black and one is yellow.

The spinner is spun once.

(a) Which colour is the spinner most likely to land on?

Answer ...... (1)

(b) The probabilities of three events have been marked on the probability scale below.

A: The spinner lands on red. B: The spinner lands on white. C: The spinner does not land on yellow.

5. Danny has two fair spinners.

Spinner A has four equal sections, two are red, one is yellow and one is green. Spinner B has six equal sections, three are red, one is yellow and two are green.

yellow red yellow

red red green red

green red green

Spinner A Spinner B

Danny spins each spinner once.

(a) Which colour is Spinner A most likely to land on?

Answer ...... (1)

(b) Which spinner is more likely to land on yellow, Spinner A or Spinner B?

Give a reason for your answer.

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...... ………………………………………………………………………… (1)

(c) What is the probability that Spinner A lands on green?

Answer ...... (1)

(d) The probabilities of three events have been marked on the probability scale below.

R: Spinner B lands on red Y: Spinner B lands on yellow G: Spinner B lands on green

6. A game involves choosing tiles from a bag. There are five tiles in the bag, as shown. A X T E X

Chris chooses two tiles at random from the bag.

(a) List all the possible outcomes of choosing two tiles.

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...... ………………………………………………………………………… (3)

(b) What is the probability that they have different letters?

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Answer ...... (2) 7. (a) There are four socks in a drawer. Success:

A B C D

Target: (i) Two socks are chosen at random. One possible choice is A and B. Write down the other five possible choices.

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(ii) Two of the socks in the drawer are white and two are black. If two of these four socks are chosen at random, what is the probability that a black pair will be chosen?

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...... (3)

(b) Another drawer contains red socks and green socks. The probability of choosing a red pair is 0.33. What is the probability that a red pair will not be chosen?

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The Robert Smyth School 4 The Robert Smyth School Topic 1 Mathematics Faculty Probability HW2 – Grade D Innovation & excellence (1)

Combined outcomes, probability addition and not probability Teacher 1. Lucy has two ordinary, fair dice. One dice is red and the other is blue. Assessment

She rolls each dice once and adds the scores to get the total.

(a) Complete the table to show the totals.

Blue dice

1 2 3 4 5 6

Red dice 3

(b) What is the probability that Lucy gets a total of 12? Answer ...... (1)

(c) What is the probability that Lucy gets a total of 6? Answer ...... (2)

2. Idnan is playing a game with a fair triangular spinner labelled 1, 2 and 3 and a fair six-sided dice.

Idnan spins the spinner and throws the dice.

He adds the number that the spinner lands on to the number shown on the dice to get his score.

(a) Complete the table to show all the scores that Idnan can get.

Number shown on dice

1 2 3 4 5 6

Number spinner lands on 2

(b) Write down the probability that Idnan scores 9.

Answer ...... (1)

(b) Write down the probability that Idnan scores less than 6.

Answer ...... (2)

(Total 5 marks)

3. Ashraf is playing a game with a fair coin and a fair triangular spinner with sections numbered 2, 3 and 4.

He flips the coin and then spins the spinner.

If the coin shows heads, his score is the number on the spinner multiplied by 3. If the coin shows tails, his score is the number on the spinner.

(a) Complete the table to show all the possible scores that Ashraf can get.

Spinner

Heads Coin Tails

(b) Write down the probability that Ashraf gets a score of

(i) 9, Answer ...... (1)

(ii) 6 or less......

Answer ...... (2) 4. A fair coin is thrown and a fair dice is rolled.

If the coin shows heads, the score is the number shown on the dice. If the coin shows tails, the score is double the number shown on the dice. (a) Complete the table to show each possible score.

Dice 1 2 3 4 5 6

Coin Heads 1 Tails 8 (2)

(b) What is the probability of getting a score of 10? Answer ...... (1)

(c) What is the probability of getting a score of less than 6?

Answer ...... (2) 5. Gemma has a box of red, blue and green pencils. She chooses a pencil at random. The probability that she chooses a red pencil is 0.5 The probability that she chooses a blue pencil is 0.2 (a) What is the probability that Gemma chooses a pencil that is either red or blue?

...... …………………………………………………………………………

Answer ...... (1) (b) What is the probability that she chooses a green pencil?

...... …………………………………………………………………………

Answer ...... (2) (c) There were ten pencils in the box originally. How many pencils were green?

...... …………………………………………………………………………

The Robert Smyth School 7 The Robert Smyth School Topic 1 Mathematics Faculty Probability Innovation & excellence Answer ...... ….. (2)

6. Jamal, Des, William and Sue play a board game. There is only one winner.

The probability that Jamal wins is 0.3 The probability that Des wins is 0.1 (a) Calculate the probability that either William or Sue wins.

...... …………………………………………………………………………

Answer ...... (2) (b) William is twice as likely to win as Sue.

What is the probability that Sue wins?

...... …………………………………………………………………………

Answer ...... (2) 7. Fiona picks a card at random from a special pack. Each card has one shape on it. The table shows the probability of each shape being picked.

Shape Probability Circle 0.6 Cross 0.25 Square 0.05 Triangle 0.1

(a) What is the probability that Fiona picks a card that does not have a circle on it?

...... …………………………………………………………………………

Answer ...... (1)

(b) What is the probability that Fiona picks a card with either a circle or a cross on it?

...... …………………………………………………………………………

Answer ...... (2)

Success: Target:

The Robert Smyth School 8 The Robert Smyth School Topic 1 Mathematics Faculty Probability Innovation & excellence HW3 – Grade C

Probability and Expectation

1. Alan, Bob and Colin play a game of darts. Teacher There is only one winner. Assessment The probability that Alan wins the game is 0.3 The probability that Bob wins the game is 0.5 (a) Write down the probability that Alan does not win the game.

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Answer ...... (1) (b) What is the probability that Alan or Bob wins the game?

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Answer ...... (1) (c) Alan, Bob and Colin play 20 games of darts. How many games would you expect Colin to win?

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Answer ...... (4) (Total 6 marks) 2. A game is played with a coloured spinner.

Blue Green

Red White

The Robert Smyth School 9 The Robert Smyth School Topic 1 Mathematics Faculty Probability Innovation & excellence The arrow is spun once. The table shows some of the probabilities of the arrow landing on a colour.

Colour Probability Red 0.4 Blue 0.2 Green 0.3 White

(a) Calculate the probability that the arrow lands on red or blue.

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Answer ...... (2) (b) Calculate the probability that the arrow lands on white.

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Answer ...... (2) (c) The arrow is spun 250 times. Calculate the number of times you would expect the arrow to land on red or green.

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Answer ...... (3) (Total 7 marks) 3. Red, blue, white and green tickets are sold in a raffle. The table shows some of the probabilities of these tickets winning the first prize.

Ticket colour Probability of winning first prize Red 0.4 Blue 0.2 White 0.1 Green

(a) Calculate the probability of a green ticket winning the first prize.

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Answer ...... (2)

(b) There were 1000 tickets sold in this raffle.

Calculate how many red tickets and blue tickets were sold altogether.

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Answer ...... (2) (Total 4 marks)

4. A school has 1260 students.

2 The probability that a student at the school has blue eyes is . 5

Calculate how many students at the school have blue eyes.

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Answer ...... (Total 2 marks) 5. In a survey about favourite methods of travel people could choose car, train, coach or aeroplane. The following probabilities were calculated from the results.

Method of travel Probability Car 0.45 Train Coach 0.17 Aeroplane 0.12

200 people took part in this survey.

How many chose train?

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Answer …………………………………...... (Total 4 marks)

The Robert Smyth School 11 The Robert Smyth School Topic 1 Mathematics Faculty Probability Innovation & excellence 6. A bag contains 200 coloured discs. The discs are either red, blue or yellow. There are 86 red discs in the bag. The probability that a blue disc is chosen from the bag is 0.22

Calculate the number of yellow discs in the bag.

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Answer ...... (Total 4 marks)

7 A scout group organises a game to raise money. 200 people each pay £2 to play the game. 1 The probability that a person wins is 10 . The winners each receive £5 and there are no other prizes.

Calculate how much profit the scout group makes from this game.

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Answer £ ...... (Total 4 marks)

Success: Target:

The Robert Smyth School 12 The Robert Smyth School Topic 1 MathematicsHW4 – Grade Faculty C Probability Innovation & excellence Relative Probability

Teacher 1. Here are three statements about probability. Assessment Tick a box to show whether you agree or disagree with each statement. Give a reason for each answer.

6 (a) Graham says, “The probability that it will rain tomorrow is ”. 5

Agree Disagree

Reason ......

...... (1)

(b) Mandy says, “In my box of chocolates there are 13 soft centres and 15 hard centres so the 13 probability of my choosing a soft centre is “. 28

Agree Disagree

Reason ......

...... (1)

(c) Tom tosses a fair coin twice. He gets a head both times. 1 He says, “The probability that I will get a head the next time I throw the coin is ”. 8

Agree Disagree

Reason ......

...... (1) (Total 3 marks)

2. A dice is suspected of bias. Here are the results of 20 throws.

3 4 2 3 1 5 6 2 4 3 4 3 1 1 6 2 5 6 5 3

(a) Use these results to calculate the relative frequency of each score.

......

Score 1 2 3 4 5 6

Relative frequency

(b) Use the relative frequency to calculate how many times you would expect to score 3 in 60 throws of this dice.

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Answer ...... (2)

(c) Compare your answer to part (b) with the number of times you would expect to score 3 in 60 throws of a fair dice.

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(1) (Total 5 marks)

3. Twenty pupils each shuffle a pack of coloured cards and choose a card at random.

The Robert Smyth School 14 The Robert Smyth School Topic 1 Mathematics Faculty Probability Innovation & excellence The colour of the card is recorded for each pupil.

(R = Red B = Blue G = Green Y = Yellow)

B Y Y G R G R Y B B Y R B B Y B B G R Y

(a) Use these results to calculate the relative frequency of each colour.

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Colour Red Blue Green Yellow

Relative frequency

(b) Use the results to calculate how many times you would expect a blue card if 100 pupils each choose a card at random.

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Answer ...... (2) (Total 4 marks)

4. Ronnie is a snooker player. He takes 20 practice shots at potting the black ball. The table shows whether he pots the black ball ( ) or misses (×) on each shot.

Shot number 1 2 3 4 5 6 7 8 9 10 Result × × × × ×

Shot number 11 12 13 14 15 16 17 18 19 20 Result × × × ×

The Robert Smyth School 15 The Robert Smyth School Topic 1 Mathematics Faculty Probability Innovation & excellence (a) Write down the relative frequency of Ronnie potting the black ball by using the results from

(i) his first five shots

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Answer ...... (1)

(ii) his first ten shots.

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Answer ...... (1)

(b) Ronnie states that, on average, he can pot the black ball on more than 50% of his shots.

Explain how the results from the table support his statement.

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...... (1)

In a match the first player to win 8 games is the winner. The scatter diagram shows the number of games that Ronnie won in each match and the number of hours that he practised before each match.

Number of 5 games won 4

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Number of hours

(c) Tick the box which best describes the strength and type of correlation shown in the scatter diagram.

Strong Weak No Weak Strong negative negative correlation positive positive (1)

(d) Ronnie draws a line of best fit on the scatter diagram. He uses it to estimate the number of games he would win if he practised for 4.5 hours before a match.

Explain why this is not sensible.

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...... (1) (Total 5 marks)

5. (a) Matthew has a dice with 3 red faces, 2 blue faces and 1 green face. He throws the dice 300 times. The results are shown in the table.

Red Blue Green

153 98 49

(i) What is the relative frequency of throwing a red?

.....……………………………………………………………………………..

Answer ...... (1)

(ii) Is the dice fair? Explain your answer.

.....……………………………………………………………………………..

.....…………………………………………………………………………….. (2) (b) Emmie has a dice with 4 red faces and 2 blue faces.

The Robert Smyth School 17 The Robert Smyth School Topic 1 Mathematics Faculty Probability Innovation & excellence She throws the dice 10 times and gets 2 reds. Emmie says the dice is not fair. Explain why Emmie could be wrong.

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...... …………………………………………………………………………….. (1) (Total 4 marks) 6. A spinner has a red sector (R) and a yellow sector (Y).

Yellow

The arrow is spun 1000 times, (a) The results for the first 20 spins are shown below. R R Y Y Y R Y Y R Y Y Y Y Y R Y R Y Y Y Work out the relative frequency of a red after 20 spins. Give your answer as a decimal.

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Answer ...... (2) (b) The table shows the relative frequency of a red after different numbers of spins.

Number of spins Relative frequency Success: of a red 50 0.42 100 0.36 200 0.34 500 0.3 1000 0.32

How many times was a red obtained after 200 spins?

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Answer ...... Target: (2) (Total 4 marks)

The Robert Smyth School 18