Probabilitie

We were due to start our next topic of probabilities. I have put some work together for you all to do at home.

I hope you are all looking after yourselves, I am missing teaching you and I am sure you miss your maths lessons.

If you need help with anything, email me on wbevis@yphub.org

Remember also there is a lot of great help on line, particularly bitesize.

https://www.bbc.co.uk/bitesize/subjects/z38pycw

Good luck guys!

Hope to see you all soon!

Mrs Bevis

Name :Lesson objectives Date :  Objectives  Start  During  End 

1. Write probabilities in the correct format 

     

Year 10

2. Display probabilities on a probability scale  

            

Bronze will identify correct format of probabilities Silver will use a probability scale Gold will recognise probabilities range from 0-1

Did you recognise that we use these words in every day life? I am certain you do. It is very likely most of you recognised them. It is possible you wrote a sentence for every one. Listen out for them on the news every day!

An equal chance of occurring will be

A child being a boy A coin showing tails The bus driver being female A dice throwing a prime number – there are 3 so you have an equal chance of getting a

prime.

Did your look like this?

This will be more opinionated !

The solutions are below.

1. On the probability scale below, mark

(i) with the letter S, the probability that it will snow in London in June,

(ii) with the letter H, the probability that when a fair coin is thrown once it comes down heads,

(iii) with the letter M, the probability that it will rain in Manchester next year.

0 1(Total 3 marks)

2.

Impossible Unlikely Even Likely Certain

Which word from the box best describes the likelihood of each of these events?

(a) You throw an ordinary dice and get an eight.

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

(b) You throw a coin and get a Heads.

.....................................

SOLUTIONS

.1. On the probability scale below, mark This should be near 0, although it isn’t 100% impossible so not on 0

(i) with the letter S, the probability that it will snow in London in June,

(ii) with the letter H, the probability that when a fair coin is thrown once it comes down heads, This will be exactly halfway

(iii) with the letter M, the probability that it will rain in Manchester next year. This should be near , 1 although it isn’t 100% impossible so not on 1.

0 1(Total 3 marks)

2.

Impossible Unlikely Even Likely Certain

Which word from the box best describes the likelihood of each of these events?

(a) You throw an ordinary dice and get an eight.

....Impossible.................................(1)

(b) You throw a coin and get a Heads.

...Even..................................(1)

Name :Lesson objectives Date :  Objectives  Start  During  End 2. Calculating probabilities of events 

     3. Apply probability knowledge to

calculate missing probabilities       

        Bronze will use appropriate format to write probability of an event Silver will calculate probability of an event Gold will calculate missing probabilities

Solutions

Did yours look like this?

Here are some solutions-

Solutions below. You do not need to simplify fractions when they are probabilities.

Can you name some language used in probability?

Probability is a number between ? And ?

Probability answers are in fractions and ? and ?

What will these questions look like in my GCSE? Try the two questions below from previous papers.

1. Joshua rolls an ordinary dice once. It has faces marked 1, 2, 3, 4, 5 and 6.

(a) Write down the probability that he gets (i) a 6, ………………………

(ii) an odd number, ……………………… (iii) a number less than 3, ……………………… (iv) an 8. ……………………… (4)

2. Emily has a bag of 20 fruit flavour sweets.7 of the sweets are strawberry flavour, 11 are lime flavour, 2 are lemon flavour.Emily takes at random a sweet from the bag.Write down the probability that Emily(a) takes a strawberry flavour sweet,...........................(1)(b) does not take a lime flavour sweet,...........................(1)(c) takes an orange flavour sweet............................(1)(Total 3 marks)

Answers1.(i) 1/6 (ii) ½(iii)2/6 or 1/3(iv) 0 this is impossible – the GCSE examiners love these ones.

2.a 7/20b9/20c 0

Name :Lesson objectives Date :  Objectives  Start  During  End 

1 Apply  probability knowledge to calculate missing probabilities

     2 Use the probability of events not

happening     

        Bronze will identify probabilities Silver will write probabilities in the correct format Gold will use probability of events not happening

Answers-

Solutions-

Solutions-

Solutions-

Name :Lesson objectives Date :  Objectives  Start  During  End 

1 Calculate probabilities showing all outcomes

     2 Use probabilities to estimate  

            

Bronze will calculate probabilities Silver will write probabilities in the correct format Gold will use probabilities to estimate

Solutions-

Solutions-

What do they look like in an exam? Here are some GCSE questions from previous papers.

1. The probability that a biased dice will land on a five is 0.3 Megan is going to roll the dice 400 times. Work out an estimate for the number of times the dice will land on a five. .............................................. _________________________________________________________________(2 marks)

2. Jack sows 300 wildflower seeds. The probability of a seed flowering is 0.7 Work out an estimate for the number of these seeds that will flower. ...................................................... _____________________________________________________________(2 marks)

Answers

1. 400 x 0.3 = 120 so 120 times is your estimate.2. 300 x 0.7 = 210 so 210 flowers is your estimate.

Name :Lesson objectives Date :  Objectives  Start  During  End 

1 Identify when events are mutually exclusive 

     2 Demonstrate use of mutually

exclusive probability rules       

        Bronze will identify mutually exclusive events Silver will write probabilities in correct format Gold will calculate probability of mutually exclusive events

Try these I have done the first one for you.

Solutions below

Solutions-

P(club) = 13/52 = ¼ P(heart or spade) = ¼ + ¼ = 1/2

P(picture) = 12/52 = 3/13 p(9 or 2) = 4/52 + 4/52 = 8/52 = 2/13

P(queen) = 4/52= 1/13

Here are some examples of mutually exclusive events from GCSE questions. I have done the first one for you.

1. A box contains sweets which are red or green or yellow or orange.The probability of taking a sweet of a particular colour at random is shown in the table.

Colour Red Green Yellow OrangeProbability 0.25 0.1 0.3

Sarah is going to take one sweet at random from the box.Work out the probability that Sarah will take an orange sweet.

...0.35.......................(Total 2 marks)

0.25 + 0.1 +0.3 = 0.65

P(orange) must be 1 - 0.65 as all possible outcomes must make 1. My answer is 0.35

2. Four teams, Chelsea, Rovers, Town and United play a competition to win a cup. Only one team can win the cup.

The table below shows the probabilities of City or Rovers or Town winning the cup.Chelsea Rovers Town United0.38 0.27 0.15 x

Work out the value of x..........................

(Total 2 marks)

3. Mr Brown chooses one book from the library each week.He chooses a crime novel or a horror story or a non-fiction book.

The probability that he chooses a horror story is 0.4The probability that he chooses a non-fiction book is 0.15Work out the probability that Mr Brown chooses a crime novel.

…………………….(Total 2 marks)

4. Here is a 4-sided spinner.

The sides of the spinner are labelled 1, 2, 3 and 4.The spinner is biased.The probability that the spinner will land on each of the numbers 2 and 3 is given in the table.The probability that the spinner will land on 1 is equal to the probability that it will land on 4.

Number 1 2 3 4Probability x 0.3 0.2 x

(a) Work out the value of x.(b) x = ………………….

(2)Sarah is going to spin the spinner 200 times.(b) Work out an estimate for the number of times it will land on 2………………(2)

ANSWERS

1. 0.352. 0.38+0.27+0.15= 0.80 take that from 1 so 1-0.80 = 0.2 3. 0.4+0.15=0.55. Take that from 1 so 1-0.55 =0.454. a 0.3+0.2=0.5. take that from 1 so 1-0.5 =0.5.

But there are 2x. Therefore 2x = 0.5 so x = 0.25

b 200 x 0.3= 60

Name :Lesson objectives Date :  Objectives  Start  During  End 

1 Estimate results from trials 

     2 Calculate probabilities from

independent events.      

        Bronze will identify use probabilities to estimate events Silver will use correct format to calculate probabilities of independent events Gold will accurate find probabilities from independent events Before we look at independent events let’s remind ourselves about mutually exclusive events. The following questions are tricky, I have done the first one for you.

Independent events When the first event has no impact on the

probability of the next Probabilities of independent events can be

multiplied to find the probability of one AND the other both happening

P(A and B) = P(A) × P(B)An example could be probability of Mrs Bevis eating a banana at lunch is ¼. The probability of Lucas having baked beans (yuk) is 9/10. These two events are not related to eachother. Therefore, the probability both happen is ¼ x 9/10= 9/40.

The probability of him leaving the plate in my room is another story!!!

Here is another example

by Unknown

Try these ones

And here’s the solutions

What about if there are so many outcomes of an event we don’t know the probability of it happening? Then we can make a diagram to list them.

Look at these events. I have listed the possible events for the first one. Can you complete it?

SolutionsYou should have 2 outcomes for the coin – heads and tails.You should have 5 outcomes for the spinner – each colour.

List all the possible outcomes of these events:1) A score in a maths quiz that is marked out of 10

2) Flipping a coin three times in a row

Did you get 11 outcomes for the first one? 0-10

And for the second did you get 8?HHH HTH TTTHHT THH TTHHTT THT This is tricky and when there are many events we put them in a table. Try these questions, I have done the first one for you.

1) What is the probability of getting a total more than 5? 26/36 as 26 results are over 5

2) What is the probability of getting a total less than 10?3) What is the probability of getting a total that is a square number?4) What is the probability of getting an even total?5) What is the probability of getting an odd total?6) What is the probability of getting a total less than 13?

Solutions2 30/36 – there are 30 numbers under 10

3.7/36- square numbers are 4 (2x2) and 9(3x3) 4. 18/36- (18 are odd) 5. 18/36 (18 are even) 6. 1 - every number is under 13.

Name :Lesson objectives Date :  Objectives  Start  During  End 

1 Represent outcomes on a space diagram 

     2 Calculate probabilities from a

space diagram       

        Bronze will draw calculate from a space diagramSilver will draw a space diagram for probabilities Gold will accurate calculate probabilities

Did your table look something like this?

+ 2 4 6 81 3 5 7 93 5 7 9 115 7 9 11 137 9 11 13 15

This question is from a GCSE paper. Try it out.1. Joe rolls a 6-sided dice and spins a 4-sided spinner.

The dice is labelled 1, 2, 3, 4, 5, 6

The spinner is labelled 1, 2, 3, 4

4

Joe adds the score on the dice and the score on the spinner to get the total score. He records the possible total scores in a table.

+ 1 2 3 4 5 6

1 2 3 4 5 6 7

2 3

3 4

4 5

(a) Complete the table of possible total scores.(2)

(b) Write down all the ways in which Joe can get a total score of 5One of them has been done for you.

(1, 4), .....................................(2)

(c) Write down all the ways Joe can get a total score of 8 or more.

…………………......................................(2)

Solution

1. (a) 4 5 6 7 8 25 6 7 8 96 7 8 9 10

(b) (1, 4); (2, 3); (3, 2); (4, 1)

(c) (2, 6); (3, 5); (3, 6); (4, 4); (4, 5); (4, 6)