Mathematical Literacy Level 4 Module 15

Mathematical Literacy NQF 4 Downloaded from hlayiso.com Maths Lit NQF Level 4

Interpreting the implication of likelihood Module 15 Downloaded from hlayiso.com Maths Lit NQF Level 4

Overview 15.1 Understanding different terms in probability 15.2 Recognising the expressions of likelihood Downloaded from hlayiso.com Maths Lit NQF Level 4

Understanding different terms in probability Unit 15.1 Probability Probability is the study of events that are not known for certain. It refers to how likely an outcome for a certain event is. Probability is commonly referred to as likelihood. Downloaded from hlayiso.com Maths Lit NQF Level 4

Understanding different terms in probability Unit 15.1 Event An event is a happening / an activity that has outcomes or results. Flipping a coin and getting Heads is one of two possible outcomes. The two possible outcomes of flipping a coin are Heads or Tails. Downloaded from hlayiso.com Maths Lit NQF Level 4

Understanding different terms in probability Unit 15.1 Outcome An outcome is a possible result of an event e.g. the outcome of selecting a dark chocolate from a box of dark and light chocolates. Downloaded from hlayiso.com Maths Lit NQF Level 4

Probability scale Unit 15.1 Probability Scale A probability scale is a graphic representation of the probability of an event. The scale can be described in words or numbers. Very Even Impossible Unlikely Likely Very Likely Certain unlikely chance 0 0,2 0,4 0,5 0,6 0,8 1 0 0% 20% 40% 50% 60% 80% 100% The scale shows a continuous range of possibilities, from impossible (it definitely can’t happen) to certain (it definitely will happen), with rough descriptions of likelihood between these two poles. Halfway between them, there is an even chance of something happening. Downloaded from hlayiso.com Maths Lit NQF Level 4

Random events Unit 15.1 Random events Random events are events that are not planned or controlled by people or by other factors. When events are random, the outcome is a matter of chance and each outcome has an equal chance of happening e.g. when tossing a coin, there is an equal chance that heads or tails could come up. Downloaded from hlayiso.com Maths Lit NQF Level 4

Dependent and independent events Unit 15.1 • Two events, A and B, are independent if the outcome of the first event does not influence the outcome of the second event. e.g. if you flip a coin and the result is Heads, this does not influence the result of your next throw, which has an equal chance of Heads or Tails. • Two events, C and D, are dependent if the outcome of one event influences the outcome of the other. e.g. if your lunch box contains three biscuits and two apples, when you eat one biscuit or one apple, you reduce the number of choices you have when deciding to eat a second thing. Downloaded from hlayiso.com Maths Lit NQF Level 4

Dependent and independent events Unit 15.1 Would it be possible for No the events to happen in Dependent any order? Yes Does one event affect the No outcome of the other Independent event? Yes Dependent Downloaded from hlayiso.com Maths Lit NQF Level 4

Theoretical and experimental probability Unit 15.1 Theoretical probability Experimental probability is the calculated chance of one is based on repeating trials of an actual particular outcome from a set of experiment. possible outcomes. What SHOULD happen What DOES happen e.g. if you actually choose a pencil from the box of two red pencil crayons and five black pencil crayons, you could pick black every time! Or you could pick red once and black six times. • If you repeated the experiment enough times, your experimental Downloaded probability and from hlayiso.com your theoretical probability might eventually be the same Maths Lit NQF Level 4

Example 15.2 page 309 Unit 15.1 Mbuso is sure that it is more difficult to throw a six on the die than any other number. He throws the die 30 times to see if he is right. These are his results: 1, 4, 4, 3, 5, 6, 4, 1, 3, 5, 5, 6, 2, 2, 4, 3, 6, 1, 1, 2, 2, 4, 5, 3, 6, 4, 2, 1, 2, 3 a) What is the theoretical probability of getting a 6? b) What is the experimental probability outcome of Mbuso’s trials? c) Write the theoretical probability and the experimental probability as percentages. d) Based on these trials, what is the experimental probability of getting an even number? Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 15.2 page 309 Unit 15.1 Mbuso is sure that it is more difficult to throw a six on the die than any other number. He throws the die 30 times to see if he is right. These are his results: 1, 4, 4, 3, 5, 6, 4, 1, 3, 5, 5, 6, 2, 2, 4, 3, 6, 1, 1, 2, 2, 4, 5, 3, 6, 4, 2, 1, 2, 3 e) What is the theoretical probability of getting an even number? f) What is the probability of getting a 7? Downloaded from hlayiso.com Maths Lit NQF Level 4

Completing a table of values by using the formula or a description Unit 15.1 a) Each number on the die has one out of six or 1 chances of being thrown. 6 b) 4 = 2 30 15 1 2 c) 6 × 100 = 16,7% and 15 = 13,3% 8 d) 16 = = 53,3% 30 15 3 1 e) = 6 2 f) Probability of getting a 7 is 0. Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 15.1 Unit 15.1 Complete Exercise 15.1 on page 311 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Recognising the expressions of likelihood Unit 15.2 Making predictions about future trends based on past events • Probability is a tool to make predictions about the outcome of an event. • Predictions about the likelihood of an event are often based on experience or knowledge. • The more data we have about a situation, the more reliable the prediction can be. • The greater the number of trials of an experiment, the closer the experimental probability gets to the theoretical probability. • In business, people use probability to make decisions about whether to invest, based on predictions of the risk of the investment. Downloaded from hlayiso.com Maths Lit NQF Level 4

Recognising the expressions of likelihood Unit 15.2 Tests with a chance of inaccurate results • Tests such as medical screening tests, pregnancy tests, drug tests and blood alcohol tests are very accurate, but there is always a small probability that the results are wrong. Sometimes there are underlying reasons for the test to be wrong. • When you have a test that with a ‘Yes’ or ‘No’ (positive or negative) result, such as a medical test, there is a small chance that: • it could be wrong when the result is ‘Yes’. • it could be wrong when the result is ‘No’. Incorrect results are usually very unlikely, but not impossible. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 15.4 page 312 Unit 15.2 Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 15.2 Unit 15.2 Complete Exercise 15.2 on page 313 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Module assessment Module 15 Complete Module assessment on page 315 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

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