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Probability Probability In this chapter will be: Certain, impossible or possible Equally likely outcomes Using numbers to represent probability Calculating probabilities The probability of something not happening Experimenting with probability Probability Lesson 1 Objective: To use the vocabulary of probability when interpreting the results of an experiment Probability Starter: Four people are taking part in a charity fun-run: Arthur, 63, a retired quantity surveyor, Mabel, 24, a gym instructor, Gary, 12, a school pupil and computer games expert, Linford Christie, 37, three times world 100m champion. Probability Starter: Four people are taking part in a charity fun-run: Arthur, 63, a retired quantity surveyor, Mabel, 24, a gym instructor, Gary, 12, a school pupil and computer games expert, Linford Christie, 37, three times world 100m champion. Who is most likely to win? Probability Starter: Four people are taking part in a charity fun-run: Arthur, 63, a retired quantity surveyor, Mabel, 24, a gym instructor, Gary, 12, a school pupil and computer games expert, Linford Christie, 37, three times world 100m champion. Who is most likely to win? Who is likely to come second ? Probability Starter: Four people are taking part in a charity fun-run: Arthur, 63, a retired quantity surveyor, Mabel, 24, a gym instructor, Gary, 12, a school pupil and computer games expert, Linford Christie, 37, three times world 100m champion. Who is most likely to win? Who is likely to come second ? Who is unlikely to win? Probability Certain, impossible or possible? Probability Certain, impossible or possible? To show probabilities we can use a likelihood scale, like this: Probability Certain, impossible or possible? To show probabilities we can use a likelihood scale, like this: Impossible Unlikely Even chance Likely Certain Probability Where is the likelihood of … (a) The next person to book a holiday will be male? Impossible Unlikely Even chance Likely Certain Probability Where is the likelihood of … (a) The next person to book a holiday will be male? Impossible Unlikely Even chance Likely Certain (a) Probability Where is the likelihood of … (b) It will snow in Australia on Christmas Day this year? Impossible Unlikely Even chance Likely Certain (a) Probability Where is the likelihood of … (b) It will snow in Australia on Christmas Day this year? Impossible Unlikely Even chance Likely Certain (b) (a) Probability Where is the likelihood of … (c) A woman will captain the women’s rugby team? Impossible Unlikely Even chance Likely Certain (b) (a) Probability Where is the likelihood of … (c) A woman will captain the women’s rugby team? Impossible Unlikely Even chance Likely Certain (b) (a) (c) Probability Where is the likelihood of … (d) A train will be late tomorrow? Impossible Unlikely Even chance Likely Certain (b) (a) (c) Probability Where is the likelihood of … (d) A train will be late tomorrow? Impossible Unlikely Even chance Likely Certain (b) (a) (d) (c) Probability Where is the likelihood of … (e) You can learn Japanese in one day? Impossible Unlikely Even chance Likely Certain (b) (a) (d) (c) Probability Where is the likelihood of … (e) You can learn Japanese in one day? Impossible Unlikely Even chance Likely Certain (e) (b) (a) (d) (c) Probability Now try … Impossible Unlikely Even chance Likely Certain (e) (b) (a) (d) (c) Probability Using numbers to represent probabilities The Probability Scale 0 0.5 1 Impossible Evens Certain Draw a line 10cm long and mark off every centimetre. The Probability Scale 0 0.5 1 Impossible Evens Certain Draw a line 10cm long and mark off every centimetre. 0, for impossible, is marked at the left hand end. The Probability Scale 0 0.5 1 Impossible Evens Certain Draw a line 10cm long and mark off every centimetre. 0, for impossible, is marked at the left hand end. 0.5, for evens, is marked in the middle. The Probability Scale 0 0.5 1 Impossible Evens Certain Draw a line 10cm long and mark off every centimetre. 0, for impossible, is marked at the left hand end. 0.5, for evens, is marked in the middle 1, for certain, is marked at the right hand end. The Probability Scale 0 50 100 Impossible Evens Certain Certain can also be called 100% and evens, 50%. The Probability Scale 0 0.5 1 Impossible Evens Certain Now do some questions… Probability Lesson 1 Plenary: Probability uses numbers to represent the chance that something will happen Probability Lesson 1 Plenary: Probability uses numbers to represent the chance that something will happen All probabilities have a value from 0 to 1 (or 0% to 100%) Probability Lesson 1 Plenary: Probability uses numbers to represent the chance that something will happen All probabilities have a value from 0 to 1 (or 0% to 100%) Probabilities can be represented on a scale THE END Probability Lesson 2 Objective: To find and record all possible outcomes for single events in a systematic way. Probability Events and Outcomes Starter List all the outcomes for the following events: List all the outcomes for the following events: Choosing a person from this group List all the outcomes for the following events: Choosing a fruit List all the outcomes for the following events: Throwing one die List all the outcomes for the following events: Throwing one die Throwing both dice List all the outcomes for the following events: Choosing a card from this hand Probability Now try … Probability Calculating Probabilities What is the probability of … Throwing a 3 with one die? What is the probability of … Throwing a 3 with one die? Throwing an odd number? What is the probability of … Throwing a 3 with one die? Throwing an odd number? Throwing seven with two dice? What is the probability of … Throwing a 3 with one die? Throwing an odd number? Throwing seven with two dice? Throwing fifteen with two dice? What is the probability of … Choosing a face card from this hand? What is the probability of … Choosing a face card from this hand? Choosing a red card from this hand? What is the probability of … Choosing a yellow crayon? What is the probability of … Hitting a number in the three times table (a multiple of three)? What is the probability of … Choosing a vowel from this sign? Probability Now try … Probability Probabilities that add to 1 What is the probability of … Not throwing a 3 with one die? What is the probability of … Not choosing a face card from this hand? What is the probability of … Not choosing a yellow crayon? What is the probability of … Choosing a consonant (not a vowel) from this sign? Probability Remember: The probability of something not happening is 1 – the probability it will happen Probability Now try … Probability Experimenting with probability Probability What experiment shall we do? Probability Copy the results into your book Probability Copy the table into your book Result Tally Frequency Heads Tails Probability Toss a coin ten times and record the results in your table. Result Tally Frequency Heads Tails Probability Toss a coin ten times and record the results in your table. Result Tally Frequency Heads Tails Use these results to calculate the experimental And theoretical probability of landing on heads. Probability Now try some questions Probability - Plenary In this chapter we have looked at: Certain, impossible or possible Equally likely outcomes Using numbers to represent probability Calculating probabilities The probability of something not happening Experimenting with probability Probability - Plenary In this chapter we have looked at: Certain, impossible or possible Equally likely outcomes Using numbers to represent probability Calculating probabilities The probability of something not happening Experimenting with probability Do you understand all of these topics? Probability Homework: Revise all of the new material for a test next lesson. To do this you should produce at least half a page of revision notes. Probability THE END Probability