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**Probability 1: the idea of probability**

IB Studies Adrian Sparrow

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**How to write a probability**

Probabilities are written as fractions or decimals. A probability will never exceed 1 or be less than 0. A probability close to 1 is very likely, if it is 1 it will be certain. A probability close to 0 is very unlikely, if it is 0 it will be impossible. A probability of 0.5, or a half has an even chance.

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Outcomes Questions Outcomes are all the things that could happen. 1. 10 different sweets are in a bag. If one is chosen, how many outcomes are there? For example when a normal fair die is rolled there are 6 outcomes: 1,2,3,4,5,6. 10 2. There are 15 students in a class. One is chosen, how many outcomes are there? When a coin is tossed there are 2 outcomes: head or tail. 15 3. 3 red counters, 2 blue counters and 1 white counter are in a bag. One is chosen. How many outcomes are there? 6

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**Favourable outcomes and expressing probabilities**

Favourable outcomes are the ones that are required, usually from the question. 2. 4 red counters, 3 blue counters and 1 white counter are in a bag. One counter is chosen at random. Find the probability of getting a blue counter. Examples 1. A fair normal die is rolled, find the probability that a 5 occurs.

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Question set 1 1. A fair normal die is rolled. Find the probability that, 2. A class of 20 students has 5 Americans, 10 Egyptians, 3 Canadians, and 2 French students. A student is chosen at random. Find the probability of the student being, a) a 4 occurs, b) an even numbers occurs, a) American, c) an square number occurs, b) French, d) a prime number occurs, c) Canadian, e) a 7 occurs. d) British.

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**Probabilities from observations**

Probabilities are not always theoretical, as the previous slides. They may be based on some surveys. For example: A student does a survey to find the colour of 50 cars parked in a staff car park. The results are shown below. Colour Silver Blue Black Other Frequency 20 12 13 5 Another car is driven into the car park. Based on the results of the survey, find the probability that the car will be, b) black, c) a colour other than silver, blue or black. a) blue,

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**Complementary probabilities**

All probabilities must add up to 1. Questions 4 red counters, 3 blue counters and 1 white counter are in a bag. One counter is chosen at random. a) Find the probability of getting a blue counter. 1. From a group of students it is known that the probability of choosing a female is 0.3. Find the probability of choosing a male. b) Find the probability of not getting a blue counter.

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**A sample space - more than 1 event**

Two dice are rolled and the scores are added. How many outcomes are there? The best way to show all the outcomes is to draw a table. When two dice are rolled and the scores are added, find the probability of getting, 1 2 3 4 5 6 7 8 9 10 11 12 a) a 2, b) a 7, c) a 10, This is the main body of the table, showing the 36 outcomes. d) a 1.

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Question set 2 Two dice are rolled and the difference of the numbers is found. Use your table to find the probability of getting a score of, a) How many outcomes are there? c) 3, b) Produce a sample space (table) to list all the outcomes. d) a prime number, 0 and 1 are not prime. 1 2 3 4 5 6 e) a non-prime number, f) not a 3.

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Expectation Expectation can sometimes be asked. This is how many times we may expect in theory something to happen, and can be found by using probability. If a die is rolled 36 times, how many times would you expect a 5 to occur? If a die is rolled 720 times, how many times would you expect a 5 to occur? Examples If a die is rolled 6 times, how many times would you expect a 5 to occur? You can use probability to answer this: If a die is rolled 12 times, how many times would you expect a 5 to occur? If a die is rolled 324 times, how many times would you expect a 5 to occur?

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Question set 3

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