How many words can you find relating to probability? Starter How many words can you find relating to probability? 1 – 4 = Good 5 – 8 = Ace 9 – 12 = Awesome 13 + = Superstar!

Impossible Could Likely Poor Even Would More Definite Probable Good Unlikely May Chance Won’t Never Certain Possible Might Improbable Less

Match the labels to the correct place on the probability scale 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 likely unlikely certain impossible even chance 100% chance no chance 75% chance 50% chance 25% chance

Use the words to describe the probabilities of the events below: You will celebrate your 10th birthday tomorrow. Tomorrow you will have a cold. It will rain tomorrow. You will be struck by lightning tomorrow. You will have something to drink tomorrow. Sometime tomorrow you will watch television. The next person you pass in the corridor will be male. The sun will rise tomorrow morning. Rolling the number six on a dice on one throw. You will still be alive when you are 100. Impossible ? Likely Unlikely Certain Even chance

To be more accurate, we express probability as a number Sometimes words aren’t enough! We’re mathematicians! How can we be more accurate when talking about probability? To be more accurate, we express probability as a number

The probability that an event will happen is a number between 0 and 1 The probability for an event which is CERTAIN = 1 The probability for an event which is IMPOSSIBLE = 0 1 5 0.2 20% Probability can be expressed as a fraction, a decimal or a percentage

Example 1 1 2 or 0.5 If I had a bag containing an apple and a pear, what is the probability that I will pick out the pear? or 50%

Example 2 A box contains 3 bags of salt and vinegar crisps, 4 bags of cheese and onion crisps and 2 bags of beef crisps. One of these bags of crisps is taken from the box at random. Work out the probability that the bag of crisps will be: a) salt and vinegar b) cheese and onion c) beef 3/9 4/9 2/9

Number of ways of achieving success Number of possible outcomes Answers Event Number of ways of achieving success Number of possible outcomes Probability Throwing a 2 1 6 1 6 Throwing a 5 Throwing an odd number 3 3 6 Throwing more than 3  3   3 6 Throwing less than 5  4   4 6 Throwing 2 or more  5   5 6 Throwing a 7  0   0 6 = 0 Throwing an even number Throwing less than 7  6   6 6 = 1

It is impossible that Ethan will take a red sweet from… Bag 4 Bag 2 Bag 5 Bag 1

It is unlikely that Ethan will take a red sweet from… Bag 4 Bag 2 Bag 5 Bag 1

It is even chance that Ethan will take a red sweet from… Bag 4 Bag 2 Bag 5 Bag 1

What is the probability of choosing a red counter from this bag? 7/5 4/12 7/12 1/11

What is the probability of choosing a yellow counter from this bag? 7/5 4/12 1/12

What is the probability of choosing a green counter from this bag? 7/5 4/12 1/12

What is the probability of this spinner landing on pink? 1/12 1/6 2/6

What is the probability of this spinner landing on yellow? 2/6 1/3 2/4 1/6

What is the probability of this spinner landing on light blue? 1 2/6 3/12 3/6

What is the probability of this spinner NOT landing on pink? 3/6 5/6 1/6

What is the probability of choosing the letter A at random from the word 2/12 3/11 2/11 2/9 MATHEMATICS

What is the probability of choosing a vowel at random from the word 3/11 3/10 4/7 4/11 MATHEMATICS

What is the probability of choosing a consonant at random from the word 4/11 7/11 7/4 4/7 MATHEMATICS

Mutually Exclusive Events What does mutually exclusive mean? Mutually exclusive means “can’t happen at the same time” So, mutually exclusive events are events that cannot happen at the same time Ask pupils for their own example of a mutually exclusive event Ask pupils for an example of events that aren’t mutually exclusive.. Eg drawing a king and a heart from a deck of cards

Turning left or turning right For example Turning left or turning right Going to Liverpool at 9am tomorrow, or going to Manchester at 9am tomorrow (You cannot turn left and right at the same time, or be in two places at once!)

What is not Mutually Exclusive Turning left and scratching your head can happen at the same time Kings and Hearts, because you can have a King of Hearts

The following statements are mutually exclusive… True or false?

True Question 1 Winning a football match AND Losing the same football match True

False Question 2 Having pizza for dinner AND Having ice cream for pudding False

Question 3 Getting the bus AND Missing the bus True

Question 4 Watching a comedy DVD AND Watching a romance DVD False

Question 5 Being awake AND Being asleep True

Rolling a number less than 3 Question 6 Rolling a 2 on a dice AND Rolling a number less than 3 False

True Question 7 A traffic light being red AND A traffic light being green True

The same baby being a girl Question 8 A baby being a boy AND The same baby being a girl True

Randomly picking a dog from the pound Question 9 Randomly picking a dog from the pound AND The dog being brown False

False Question 10 Me not winning the lottery AND My friend not winning the lottery False

Probability Bingo Aim: Full House Grid: 9 Grid Play: Calculate probability & cross it off

Numbers to Use ¼ 0.42 5/6 12% 0.35 ½ 7/15 0.62 30% 13/20 0.4 57% ¼ 0.42 5/6 12% 0.35 ½ 7/15 0.62 30% 13/20 0.4 57% ¾ 1/3 55% 0.34

Probability of scoring less than 6 on a normal dice

The probability that I will set homework is 0. 66 The probability that I will set homework is 0.66. What is the probability I will not set homework?

The chance of picking a girl from a group of 3 girls and 7 boys.

There are 4 white beads, 2 red beads, 1 green bead and 8 blue beads What is the probability that the bead I pick is NOT blue?

The chance of getting 2 heads when 2 coins are flipped.

The probability that I choose a girl to answer a question is 0 The probability that I choose a girl to answer a question is 0.58 what is the probability I choose a boy?

Tonight I can go to the cinema, visit a friend or stay at home. I am equally likely to do each thing What is the probability I stay at home?

What is the probability of getting a prime number when a normal dice is thrown?

I have red, green and black socks The probability I wear red socks is 0.15 The probability I wear green socks is 0.23 I am going to wear socks. What is the probability I wear black socks?

At a running club 25% of the runners have run a marathon. What is the probability a runner picked at random has not run a marathon?

A box of chocolates has 5 strawberry creams, 4 coffee creams, 9 caramels and 2 toffee dreams. What is the probability that I pick a coffee cream or a caramel?

In an experiment a drawing pin lands point down 9 times out of 20. What is the experimental probability that the pin will land point up?

The probability that it rains tomorrow is 0. 43 The probability that it rains tomorrow is 0.43. What is the probability that it will NOT rain?

In a year group of 200 students 70 are left handed In a year group of 200 students 70 are left handed. What is the probability that a randomly picked student will be left handed?

In a group of 50 teachers 6 are mathematicians. What is the probability that a teacher picked at random will be a mathematician?

I observe 100 cars. I see 40 red cars I observe 100 cars. I see 40 red cars. Use relative frequency to estimate the probability that the next car I see will be red.

What does exhaustive mean? Exhaustive Events What does exhaustive mean? The probabilities of all possible outcomes add up to 1. Ask pupils for their own example of a mutually exclusive event Ask pupils for an example of events that aren’t mutually exclusive.. Eg drawing a king and a heart from a deck of cards

=1 Example 1 The probability of getting a 1 is 1 6 Total: 1 6 + 1 6 + 1 6 + 1 6 + 1 6 + 1 6 =1

Example 2 A box contains 3 bags of salt and vinegar crisps, 4 bags of cheese and onion crisps and 2 bags of beef crisps. One of these bags of crisps is taken from the box at random. What is the probability they are beef? Flavour of crisp Salt & Vinegar Cheese & onion Beef Probability 3 9 4 9 1 – ( 3 9 + 4 9 ) = 2 9

Example 3 P(bus) = 1 – (0.36 + 0.52 + 0.06) = 0.06 In a survey during walk to school week, all the pupils at Winsford Academy either cycle, walk, come by bus or still come in a car. The probabilities they travel each way are below. What’s the probability they come by bus? Method of Travel Cycle Walk Bus Car Probability 0.36 0.52 0.06 P(bus) = 1 – (0.36 + 0.52 + 0.06) = 0.06

Answers – Q1 & 2 Event M or N? E? Tossing a head with a coin / Tossing a tail with a coin M E (H or T) Throwing a number less than 3 with a dice / Throwing a number greater than 3 with a dice Drawing a Spade from a pack of cards / drawing an Ace from a pack of cards N Drawing a Spade from a pack of cards / Drawing a red card from a pack of cards (Choosing from a group of three girls and two boys): Choosing two girls / choosing two boys Drawing a red card from a pack of cards / drawing a black card from a pack of cards E Winning a football match / Drawing a football match Eating toast for breakfast / Eating chips for dinner  

Answers – Q3, 4, 5 & 6 Question 3 P (not h) = 0.7 P (not h) = 0.48 0.24 Question 5 P (purple) = 0.1 P (purple) = 0.2 P (purple) = 4% P (purple) = 7/20 Question 6 P (3) = 3/8 P (red) = 1/8 i) M ii) N iii) M iv) M

Which horse is most likely to win? Why? Are there any horses that definitely won’t win? How do you know?

Which horse do you think will win? Play now with the person next to you.

+ 7 2 3 4 5 6 7 From this sample space diagram we can see that there are 36 possible outcomes when two dice are thrown. 7 3 4 5 6 7 8 4 5 6 7 7 8 9 7 5 6 7 8 9 10 Six of these have a total of 7. 7 6 7 8 9 10 11 6 P(7) = 7 36 7 8 9 10 11 12

I am choosing an outfit… How many different combinations could I have? What is the probability of choosing a red t-shirt?

So the probability of choosing a red t-shirt = Putting it in to a sample space diagram makes it a lot easier to calculate the probability   Trousers Blue Black Grey Orange T-Shirt Red White 4 16 So the probability of choosing a red t-shirt =

Now on whiteboards… Trousers Blue Black Grey Orange T-Shirt Red White   Trousers Blue Black Grey Orange T-Shirt Red White As a fraction work out the probability of: (a) Choosing a white t-shirt with either blue or grey trousers (b) Not choosing orange or blue trousers 1 8 1 2

Answers Question 1 1/12 Question 2 3/16 2/16 4/16 Question 3 15/25 Question 2 3/16 2/16 4/16 Question 3 15/25 3/25 12/25 7/25 4/25 Question 4 8/36 4/36 24/36 Question 5 2/24 6/24 7/24 1/24 5/24

True False True False True False Starter – True or False You are equally likely to get a heads or tails when flipping a fair coin True False You are more likely to get an even number when rolling a fair die The probability of picking a red card is 2/3 True The probability of landing on a 1 on the spinner is 1/4 2 5 4 3 False The probability of not picking a black card is 4/6 True The probability of choosing an ‘A’ from is 2/10 False

Ends of first and second level branches show the different outcomes. Probability Trees The probabilities for each event are shown along the arm of each branch and they sum to 1. Ends of first and second level branches show the different outcomes.

Rebecca has nine coloured beads in a bag Rebecca has nine coloured beads in a bag. Four of the beads are black and the rest are green. She removes a bead at random from the bag and notes the colour before replacing it. She then chooses a second bead. Draw a tree diagram showing all possible outcomes. Calculate the probability that Rebecca chooses: (i) 2 green beads (ii) A black followed by a green bead. First Choice Second Choice black black green black green green

Peter has ten coloured cubes in a bag Peter has ten coloured cubes in a bag. Three of the cubes are red and seven are blue. He removes a cube at random from the bag and notes the colour but does not replace it. He then chooses a second cube at random. Draw a tree diagram showing all possible outcomes. Calculate the probability that Peter chooses: (i) 2 red cubes (ii) A blue cube followed by a red cube. First Choice Second Choice red red blue red blue blue

The ‘And’ and ‘Or’ Rules Calculate the probability of picking one milk chocolate and one dark chocolate in any order. First Pick Second Pick Milk Milk Milk AND dark OR dark AND milk = 18 x 12 + 12 x 18 30 29 30 29 = 432 870 Dark Milk Dark Dark

Extension There are 4 blackcurrant sweets, 3 apple sweets and 4 strawberry sweets in a bowl. I pick two sweets (one after the other). What is the probability that I pick two sweets of the same flavour?

Answers 24 49 42 2 16 58 90 90 90

Pair Activity You are running a stall at a carnival using the pack of cards, any heart wins. At £10 a go, what would you make prize y in order to make a profit, and to make the game enticing? First Card Second Card ¼ £y ¼ Not £3 ¾ £10 ¼ £3 ¾ Not Not £0 ¾

Plenary Summarise in a text message (160 characters) what the key learning points are from today’s lesson.