(Single and combined Events) Sample Space (Single and combined Events)

What is Sample Space Sample Space refers to listing all possible outcomes of an event. Examples include: Event Sample space Throwing a coin Head, Tail Rolling a die 1,2,3,4,5 and 6. Roulette Red, Black, ‘0’

Single Event: Single Event: A single event is when there is a fixed probability on any event which only takes place once. Examples include a coin that is flipped once, a die that is rolled once and single roulette spin. A die is rolled once, what is the sample space that they roll a 5? What is the sample space that they roll a 5 or more What is the sample space that they roll less than a 5?

Answers: 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

Combined Events: Combined Events: When more than one event happens simultaneously. Examples: Tossing of two coins Drawing two spades from two decks of cards. Rolling two dice.

Sample space: Throwing two dice What is the total possible outcomes? What is the maximum total we can get? What is the sample space of rolling a total of 6? What is the sample space of rolling a total greater than 9? 36 12 (5,1);(4,2);(3,3);(2,4);(1,5) (6,4);(5,5);(4,6);(6,5);(5,6);(6,6)

Tree Diagram The previous diagram is only applicable when two events are happening as it enables one event along the ‘x’ axis and the other along the ‘y’ axis. When there is more than one event happening simultaneously, a tree diagram is used. An example of a tree diagram for a coin flipped 4 x times is shown below:

Questions What is the total number of possible outcomes? What is the total sample space for at least two heads? What is the sample space of all the flips being the same? What is the probability of the third flip being tails?

Comments What we learnt today? -

Probability Starter: In your groups, place the events Lesson Objective: To be able to calculate theoretical probability from sample space Starter: In your groups, place the events on your table in order from least likely to most likely.

Having spaghetti bolognese for dinner tonight Rolling a six Lesson Objective: To be able to calculate theoretical probability from sample space Having spaghetti bolognese for dinner tonight Rolling a six on a single die Winning The Lottery A male winning the Great British Bake Off Christmas Day falling on the 25th of December

At the races Each horse moves 1 square if you get its total when you roll both dice. Is it a fair race? Is there an equal chance of winning? 2 3 4 5 6 7 8 9 10 11 12 Dice Roller

How many possible outcomes are there? Lesson Objective: To be able to calculate theoretical probability from sample space How many possible outcomes are there? How can we list all possible outcomes? Would this be helpful? 2 + 3 = 5 1 + 1 = 2 1 + 6 = 7 1 + 2 = 3 3 + 1 = 4 2 + 1 = 3 2 + 6 = 8 1 + 5 = 6 1 + 4 = 5 2 + 4 = 6

What would be an effective way to show all possible outcomes? Lesson Objective: To be able to calculate theoretical probability from sample space What would be an effective way to show all possible outcomes?

Why isn’t the race fair? Consider the possible outcomes from finding the total of 2 dice: Dice A Total Probability 2 1 2 3 4 5 6 3 2 3 4 5 6 7 4 3 4 5 6 7 8 5 4 5 6 7 8 9 Dice B 6 5 6 7 8 9 10 7 6 7 8 9 10 11 8 7 8 9 10 11 12 9 10 11 12 7 is the most likely total, so horse 7 is most likely to win 2 & 12 are the least likely totals, so horses 2 and 12 are least likely to win

Now: Pick a worksheet based on how confident you feel! Lesson Objective: To be able to calculate theoretical probability from sample space Two spinners A and B are spun and the scores are added together. (a) Complete the sample space diagram. (b) What is the probability of scoring a total of 2? (c) What is the probability of getting an even total? (d) What is the probability of getting a total that is a multiple of 3? Now: Pick a worksheet based on how confident you feel! Green: Not very confident Amber: Quite Confident Red: Confident

Lesson Objective: To be able to calculate theoretical probability from sample space James Bond is playing a game where you must roll two dice. In order to win he either needs to roll a double (the same score on both dice) or a get score greater than 10 when you add the two dice scores together, but he has to say which he will go for before he starts. Which should he say he will go for? Remember you have to show Bond why you've chosen what you have!

Learning Objective Three Tasks To be able to calculate theoretical probability from a sample space Three Tasks Investigate the probability of the outcomes for: Rolling two dice Flipping two coins Drawing a coloured brick from a bag of ten

Two Dice Number rolled Tally Total Probability 1 2 3 4 5 6 7 8 9 10 11 12 Roll both dice an even number of times (add up the numbers) Record your results in a tally chart Estimate the probability for each result using your sample

Two Coins Flip both coins an even number of times Record your results in a tally chart Estimate the probability of all scenarios Result Tally Total Probability Both Heads Both Tails One Heads, One Tails

Ten bricks in a bag Challenge: Can you estimate the number of Take a brick from the bag Record its colour on a tally chart Place the brick back into the bag Repeat this at least 30 times Estimate the probability of drawing each colour Colour Tally Total Probability Red Blue Yellow Challenge: Can you estimate the number of each colour brick in the bag?

Learning Objective To be able to calculate theoretical probability from a sample space