2. http://www.mathsisfun.com/fractions.html Year 8 Mathematics Probability

3. Learning Intentions You should: Understand the terms impossible, unlikely, likely and certain Know that the probability scale goes from 0 to 1 Be able to calculate the probability of an event occurring Be able to calculate the probability of an event not occurring Understand the terms: experiment, event and outcome Understand the difference between experimental probability and theoretical probability Be able to calculate the number of times and event should occur

4. Probability In mathematics, the act of rolling a die, tossing a coin, choosing a counter, etc is known as an experiment. The result of the experiment will result in one of a number of outcomes. For example, when tossing a coin we could obtain a head or a tail. An event is when we obtain a particular value, for example a head.

5. Outcomes When tossing a coin, the possible outcomes are: Head or Tail When rolling a die, the possible outcomes are: 1, 2, 3, 4, 5 or 6 The month you were born in can be: Jan, Feb, Mar, Apr, May,....., Dec A baby can be: A boy or a girl When choosing a counter from a bag containing one red, two blue and three green counters can be: A red counter, a blue counter or a green counter

6. Outcomes Make a list of the outcomes from the following events: 1. Throwing a die. 2. Tossing a coin. 3. Spinning this pointer.

7. Events An event is when you carry out the experiment and obtain a value When tossing a coin, an event might be: Obtaining a head When rolling a die, an event might be: Obtaining a six

8. Probability A probability is a measurement of how likely an event is likely to occur. We can calculate the probability of an event happening using the following formula: For example, the probability of obtaining a 3 when rolling a die is:

9. Calculate the Probability What is the probability of: Getting a head when tossing a coin. P(H) = Choosing a prime number from the numbers 2 - 11 P(Prime) = Choosing a ‘B’ from the word PROBABILITY? P(B) =

10. Calculating Probability If the following spinners are spun, what is the probability of landing on the shaded section?

11. Calculating Probability Counters are placed in each of the boxes as shown below. In each case, find the probability of selecting the shaded counter.

12. Probability Scale Consider a bag containing three green counters. Since probabilities are calculated using the following equation: The probability of selecting a green counter is ____ This is a certain event. The probability of selecting a red counter is ____ This is an impossible event.

13. Probability Scale The smallest value on the probability scale is 0. The largest value on the probability scale is 1. Probabilities are written as fractions.

14. Probability Scale Draw the probability scale in your book. Indicate, using arrows labelled a to f, the probabilities for: a.Tossing a HEAD on a coin b.Cutting a SPADE from a pack of cards c.May following April d.The electricity being cut off today e.Scoring a 1 or a 6 when rolling a die f.Scoring 23 with a single dart on a dart board

15. It didn’t happen Sometimes we need to calculate the probability of an event not happening. For example, Alice has 12 cards as shown, each with shapes on them. What is the probability of Selecting a card with a triangle Not selecting a card with a triangle.

16. Not Probability We calculate the probability of an event not happening using the formula P(Event not happening) = 1 – P(Event happening) Example: Writing pads are available in 4 different colours. In a pack there are 2 blue, 2 red, 4 white and 4 green. If I open a new pack, what is the probability that I pick: a.a blue padb.a red padc.a pink pad d.not a blue pade.not a red padf.neither a blue or red pad

17. Counting Success We can use probability to calculate the number of times an event will occur. We can rearrange the probability formula to give: For example, if I roll a die 120 times, how many times would I expect to obtain a 6?

18. Experimental Probability Sometimes we cannot calculate the theoretical probability and instead we calculate the experimental probability. We use the formula:

19. Experimental Probability For example, a company makes light bulbs. When it tests a sample of 100 bulbs, it finds that, on average, 6 are faulty. Calculate the probability that a bulb will be faulty

20. Experimental Probability Eve and Ellie conduct a survey on pupil’s favourite pets. Here are the results. a.What is the probability of a pupil’s favourite pet being a: (i)cat(ii)dog(iii) fish(iv) not a dog b.If 270 pupils are asked, how many would say they preferred a cat? c.If 464 pupils are asked, how many would say they preferred a bird? d.If 38 pupils are asked, how many would say they preferred a dog? PetCatDogRabbitFish Frequency81262

21. Fair Events We consider an experiment to be fair if the experimental probability and the theoretical probability is the same. For example: the theoretical probability of tossing a HEAD is 0.5. if we toss the coin a large number of times find that the experimental probability is also 0.5, we consider the coin to be fair.

22. Biased We consider an experiment to be biased if the experimental probability and the theoretical probability are different. For example: the theoretical probability of tossing a HEAD is 0.5. if we toss the coin a large number of times find that the experimental probability not 0.5, we consider the coin to be biased. If the probability is greater than 0.5, then we are more likely to obtain a head than a tail. It is likely there is more weight on the tail side of the coin.