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The maths department are making weekly booklets for you tocomplete at home.The maths department are making booklets for you tocomplete at home

North Gosforth AcademyMathematics Home Booklet

Year 7 Higher

20th April – 1st May

The topics covered are below. You have already covered these in your maths lessons and being at home gives you a chance to revise! Create yourself a useful revision resource and practise key skills!

Instructions:

There are plenty of examples – write these down. Write down any useful facts.

Complete questions to practise the skills and stretch questions to push yourself. Show working out!

Old maths books and revision guides are useful sources of information if you have them

Any access to the internet, even limited, gives you access to Hegarty maths, Corbett maths and Mathsgenie where tutorial videos are available

Topics in this booklet:

Worded probability Calculating simple probability Probability sums to 1 Sample space diagrams

Likely, chance, certain, equal uncertain, probable, possible, impossible, good chance, poor chance, no chance, chance, even chance, evens, fifty- fifty, likelihood, probability, possibility

What is the chance of winning the national lottery? How do they work this out? Would it change if we had more or less numbers.

a) We describe the chance of something happening with the words: Impossible–unlikely–evens–likely-certain. b)We show our results on a probability line:

Impossible evens certain

1) Write out the definition of the word probability.2) Order the definitions into a list starting with the least likely to happen. Do any mean the same chance?3) Choose from the words impossible, unlikely, evens, likely or certain to describe the chance of the following happening:a) Your teacher will visit the moon tonight.b) I will get a head when I throw a fair coin.c) December will follow November this year.d) Swansea would _ _ _ _ _ beat Pontycymmer in

football.e) I will have homework at least once next week.4) Can you write one probability sentence for each of the words certain, impossible, likely, unlikely, certain.

Sally says that if only two people are in a raffle they both have the same chance to win?Liam thinks she is incorrect but does not know how to explain this to her.Can you help Liam. You must explain in complete sentences using both the key words and your mathematical understanding of chance. Some examples would help to convince Sally.

a

…SkillIf there are several balls in a bag, 4 blue, 5 green, 7 yellow and 9 pink.What is the probability of aPink?Blue?Yellow?Green?

What is the probability of not getting aNot a pink?Not a blue?Not a yellow?Not a green?

StretchI role two dice at thesame time.

What is the probability of the dice addingup to 7?

What is the probability of the total on thedice being more than 6

What is the probability the total of thetwo dice is less than 1?

Probability of an event.

LiteracyCan you write events insentence for each of the following words.Impossible, unlikely, evens, likely and certain.

Research CardsWhat is the total number of cards in

a deck? How many suits are in a deck? Identify the names of the

suits. How many picture cards, (face cards) are their in a suit? What

values can an ace stand for?

MemoryRemember mathematicians write theprobability of an event as. (The event

being what you want to happen)

Desired outcome

Total outcomes𝑃 𝑒𝑣𝑒𝑛𝑡

ProbabilityVideos 244, 245, 250 on Corbettmaths

© CORBETTMATHS 2018

Click

Examples

Workout

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Question 1: Theo has 3 red sweets and 2 white sweets.He picks a sweet at random.

(a) Write down the probability that Theo picks a red sweet.

(b) Write down the probability that Theo picks a white sweet.

Question 2: Leah has 12 cards, each with a shape on it.She takes a card at random.

(a) What is the probability that Leah takes a card with a star on it?

(b) What is the probability that Leah takes a card with a triangle on it?

(c) What is the probability that Leah takes a card with a circle on it?

Question 3: Ralph has 9 cards, each with a number on it.

He picks a card at random.Write down the probability that the chosen card is

(a) the number 8 (b) an even number (c) a number less than 7

(d) a multiple of 4 (e) a square number (f) a prime number

Question 4: There are 12 red roses, 5 yellow roses and 3 white roses in a vase.Felix takes a rose, at random, from the vase.

(a) Write down the probability that he takes a white rose.(b) Write down the probability that he takes a red or a white rose.(c) Write down the probability that Felix takes a rose that is not red.

ProbabilityVideos 244, 245, 250 on Corbettmaths

© CORBETTMATHS 2018

Question 5: Leon throws a biased coin.The probability of getting tails is 0.4 Work out the probability of getting heads.

Question 6: Edith plants a daffodil bulb.The probability that the bulb will grow is 0.8What is the probability that the bulb will not grow?

Question 7: Wycombe Wanderers play a match of football. The probability that they win the match is 0.28 The probability that they draw the match is 0.55 Work out the probability that they lose the match.

Question 8: Evelyn has 80 pens in a drawer.15 pens are black and the other pens are blue.

Evelyn picks a pen at random from the drawer.

(a) What is the probability that Evelyn picks a black pen?(b) What is the probability that Evelyn picks a blue pen?

Question 9: There are 20 counters in a bag.

2 of the counters are white. 1 of the counters is pink.4 of the counters are black.The rest of the counters are purple.

Carter takes a counter at random from the bag.Show that the probability that the counter is white or purple is

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Question 10: There are only pink, yellow, green and blue counters in a bag.The table shows the probability that a counter taken at random from the bag will be pink, green or blue.

(a) Work out the probability that the counter taken is

yellow There are 40 counters in the bag.

(b) Work out the number of blue counters in the bag.

Apply

ProbabilityVideos 244, 245, 250 on Corbettmaths

© CORBETTMATHS 2018

Question 11: Darcy has a biased spinner.A spinner has sections labelled 1, 2, 3, 4 and 5.The table below shows information about some of the probabilities

Work out the value of x.

Question 12: Frederick organises a rafYle for his school fayre.The top prize is a ride in a hot air balloon, which will be won by 1 ticket. Altogether Frederick sells 700 rafYle tickets.Miss Robinson buys 5 tickets for the rafYle.

Work out the probability that Miss Robinson does not win.

Question 13: There are 20 sweets in a box.The probability that a chocolate is picked at random from the box is 0.6 How many chocolates are in the box?

Question 14: A bag contains 600 coloured counters.The counters are yellow, brown or orange. There are 117 yellow counters in the bag.The probability that a brown counter is chosen from the bag is 0.35

Calculate the number of orange counters in the bag.

Question 1: Megan has a fair 6 sided spinner.The spinner has the letters A, B and C on it.

The probability that the spinner will land on an A is 12

The probability that the spinner will land on a C is 13

Write the letters on the spinner.

Complementary Exhaustive

Probability Mutually ExclusiveExpected Frequency

Find 5 jobs where you would calculate probabilities or risk.

Complete the sentences below

Probabilities for a single event add up to 1.You can use this to find missing probabilities, by find-

Find the missing probabilities. Answer the questions below each table ing the difference to 1.

Expected frequency = probability x number of tries You can use this to estimate how many times you

Find x.

If I spin the spinner 120 times, howmany times would you expect it to land on Green or Blue?

Find x.

If I spin the spinner 80 times, howmany times would you expect it to land on Blue?

Find x.

If I spin the spinner 80 times, how many times would you ex- pect it to land on Green orBlue?

Find the missing probabili- ties. Answer the questions below each table

Find the missing probabili- ties. Answer the questions below each table

Draw out a table for each problem. Find the miss-ing probabilities. Answer the questions below each table

1. Mary plays a game of throwing a ball at a target. In the game, you can score 0, 1 or 2. The probability that she scores 0 is 0.4. She is twice as likely to score 1 as 2. What is the probability she does not score 2?

2. There are only red counters, yellow counters, blue counters and green counters in a bag. They are in the ratio 1:2:3:4. Find the probability of picking each colour from the bag.

3. There are only blue, green and red counters in a bag. There are twice as many green counters as red counters.There are twice as many blue counters as green counters. What is the probability of not picking a red coun- ter?

4. A bag contains some 50p coins, £1 coins and 1p coins. There are 5 more 50p coins than £1 coins. There are twice as many 1p coins as £1 coins. There are 25 coins in the bag altogether. Find the probability of picking out each coin from the bag.

5. A dice is biased so that it lands on 1 one quarter of the time. It lands on 3 twice as often as it land on 2 and three times as often as it lands on 4. It lands on 5 ten percent more often than it lands on 4 and ten percent less often than it lands on 6. If I roll the dice 350 times, how often should I expect to roll a 6?

Red Green Blue Pink

Probability 0.5 0.01 0.22

What is the probability that the spinner will land on Red or Blue?

Red Green Blue Orange

Probability 0.25 0.05 0.3

What is the probability that this spinner willnot land on Red?

Dog Cat Fish Bird

Probability 1/5 1/20 3/10

What is the probability that a student cho- sen at random prefers Fish or Birds?

Red Green Blue

Probability 0.5 0.3

If I spin this spinner 30 times, how many times would you expect it to land on blue?

Red Green Blue

Probability 0.25 0.05

If I spin this spinner 80 times, how many times would you expect it to land on red?

Dog Cat Fish

Probability ¼ ½

I select 100 students at random. For how many students would you expect their fa- vourite pet to be dog?

Red Green Blue Pink

Probability 0.5 x 0.22 x

Red Green Blue Pink

Probability 0.4 0.3 2x xRed Green Blue

Probability 15x 3x 2x

StretchPeter conducts an experiment with a dice. The results are shown below:

a)b)

c)

What is the experimental probability of rolling a 5? Compare this to the theoretical probability. Do you think this dice is biased?If Peter was to roll this dice 90 times, how many times would you expect not a 5 to be rolled?

Skills Practice1) What is the probability of picking a vowel (a,e,I,o,u) from

the letters MRS MAHONEY?2) Which is more likely- rolling a prime number on an

ordinary 6 sided dice, or rolling a square number?3) There are 10 counters in a bag. 5 are red, 3 are blue

and the rest green. What is the probability that I choose:a) A green counter B) A blue Counter

C) A yellow counter D) A red or blue counter4) A spinner has the numbers 1, 2, 3 and 4 on. A second spinner has the numbers 4, 5, 6 and 7 on. The two spinners are spun and their numbers added together.

a) Draw a sample space diagram for thisb) What is the probability that the total score is

greater than 10c) What is the probability that the total score is 1

Memory

Expectation:Probability x no. of trials

Research

What is meant by the term mutually exclusive? Give an example.

LiteracyTheoretical probability Experimental probability ExpectedTrialSample space diagram

5 rolled Not a 5 rolled

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