Probability Today you will need to make sure you have Week 6 Today you will need to make sure you have White board, marker and rubber Pen Your maths folder Handed in the homework sheets.

Review of previous sessions Any questions from your homework, write down and pass to Cathy List 3 things a bar chart MUST have. Multiple the following by 10…12.45, 3, 356.3, 0.67, 70. Divide the following numbers by 10…. 10…12.45, 3, 356.3, 0.67, 70. Round the following numbers to the nearest 10… 346, 92, 749, 292, 17, 899. What can you tell me about the number 2,974,326 What is the mean and range of the following data…71, 79, 62, 68, 92, 68, 75. What is the mean and range of the following data 12, 14, 16, 16, 10, 18, 12, 22, 18, 16. Please calculate the following showing all working and a reverse check 2402 - 485 =

Think of a Number A bit of maths magic? Kindly contributed to www.skillsworkshop.org by by Fiona Campbell fiona.campbell@cityofbristol.ac.uk City of Bristol College. N1/E2.3 Add and subtract two-digit whole numbers N1/E2.4 Recall addition and subtraction facts to 10. N1/E3.3 Recall addition and subtraction facts to 20 (but makes a good warm activity for any level)

Think of a number between 1 and 10

Add 1

Double the result Hint: to double you by what?

Plus 5

Halve the result [Hint to halve something you divide by what?] ….

Add eight

Subtract 9

Subtract the number you first thought of

Your answer is 1 Try starting again with another number. Does it work for all numbers? Use big numbers and a calculator. How does it work?

What you need to know E3 –L2 Understand that some events are impossible Understand that some events are certain to happen Know that some events are more likely to occur than others Understand the concept of possible outcomes, e.g. there are two possible outcomes for the gender of a baby Understand that some events can happen in more than one way, e.g. there are three possible ways of getting an odd number with the throw of a die Understand that probability is an expression of likelihood, and use terms such as a one in two chance Understand that the likelihood of an event is measured on a scale from 0 (impossible) to 1 (certain) Understand that likelihood (or probability) is expressed as the number of ways the event can happen divided by the total number of possible outcomes Understand that likelihood or probability can be written as a fraction, decimal or percentage, e.g. the likelihood that a coin will land heads-up is 50%, .5 or 1/2 The expression there is a fifty-fifty chance is an expression of likelihood using percentages Understand that events are independent when the outcome of one does not influence the outcome of another, e.g. the gender of a baby does not influence the gender of a second one Understand that events are combined when the outcome depends on the separate outcome of each independent event, e.g. the likelihood that twins will both be girls Record the range of possible outcomes of combined events in tree diagrams or in tables

What will you learn today What will you learn today? (something you did not know yesterday) By the end of this session I will be able to… Show that some events are more likely to occur than others Express the likelihood of an event using fractions, decimals and percentages with the probability scale of 0 to 1 Identify the range of possible outcomes of combined events and record the information using diagrams or tables Examination style questioning Key Words

What’s the difference between chance and probability? Chance is described in words. Eg. Impossible, Unlikely, Evens, Likely, Certain Probability is given a numerical value. Probability is given as a fraction, decimal or percentage.

What is a probability scale? This is a line where events can be placed to show the chance or probability of an event occurring. Impossible Certain 3 4 1 4 1 2 1

Getting a C for GCSE Maths Throwing a 6 on a dice Tossing a coin and …getting “heads” It will rain tomorrow Winning the lottery Impossible Certain All probabilities lie somewhere on a scale between “Impossible” and “Certain” Ordering probability of events activity.

1 Getting a C for GCSE Maths Throwing a 6 on a dice Tossing a coin and …getting “heads” It will rain tomorrow Winning the lottery Impossible Certain 1 All probabilities lie somewhere on a scale between “Impossible” and “Certain” The probability scale goes from 0 to 1

1 Passing you Functional Skills Maths Throwing a 6 on a dice Tossing a coin and …getting “heads” It will rain tomorrow Winning the lottery Impossible Certain 1 14,000,000 16 1 0.5 0.7 95% Probabilities can be expressed either as fractions or as decimals (and sometimes as percentages)

Washing Line.

The rule of probability 𝑯𝒐𝒘 𝒎𝒂𝒏𝒚 𝒘𝒂𝒚𝒔 𝒕𝒉𝒆 𝒐𝒖𝒕𝒄𝒐𝒎𝒆 𝒚𝒐𝒖 𝒘𝒂𝒏𝒕 𝒄𝒂𝒏 𝒉𝒂𝒑𝒑𝒆𝒏 𝑻𝒐𝒕𝒂𝒍 𝒐𝒖𝒕𝒄𝒐𝒎𝒆𝒔 It is often easier to give a probability as a fraction using the rule above. If you are given probabilities in decimals, then use decimals.

1 2 Example 1: Tony throws a coin. What is the probability of landing a head? number of ways of achieving success number of possible outcomes 1 2

1 6 Example 2: Amy rolls a fair dice, what is the probability of getting a four? number of ways of achieving success number of possible outcomes 1 6

The probability of throwing a 6 with a fair dice is 16 P(6) = 16 So the probability of not throwing a 6 is 56 P(not 6) = 1- 16 = 56 Whole group discussion with directed questioning.

Here’s how the rule works: A bag contains 9 blue marbles, 5 red marbles and 6 green marbles. What’s the probability of selecting a blue marble from the bag? What you want: How many blue marbles there are 9 Total outcomes: How many marbles there are in total 20

Try the skill

More than one option A bag contains 6 blue marbles, 5 red marbles and 9 green marbles. What’s the probability of selecting a green or red marble from the bag? What you want: How many green or red marbles there are 14 Total outcomes: How many marbles there are in total 20

Dice Probability

Spinner probability

1 4 Suppose I toss two coins: or I would get one of these combinations: Heads, Heads Heads, Tails Tails, Heads Tails, Tails H, H H, T T, H T, T or What is the probability of getting two heads? 1 4 Only one of these four combinations is two heads

Probability outcomes T, T T, H T H, T H, H H Second Coin First Coin A Sample Space is a list of all the possible outcomes, e.g. HH, HT, TH, TT T, T T, H T H, T H, H H Second Coin First Coin We can show this in a Sample Space Diagram: There are 4 possible outcomes if you toss a coin twice So the probability of two heads is ¼

Tree diagrams. If I roll a dice, what is the probability the result will be even? 3 6 3 ÷ 6 = 0.5 Even Check the results add up to 1 0.5 + 0.5 = 1 Odd 3 6 3 ÷ 6 = 0.5

Please don’t write on the worksheets Individual Study Choose which areas to develop depending on your own strengths and areas identified from your diagnostic Computers available Please don’t write on the worksheets

Reflection of the lesson What did you learn new today? Why did you learn it? How are you going to remember it?