Presentation on theme: "Probability 1: the idea of probability"— Presentation transcript:
1 Probability 1: the idea of probability IB StudiesAdrian Sparrow
2 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.
3 OutcomesQuestionsOutcomes 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: 1,2,3,4,5,6.102. 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.153. 3 red counters, 2 blue counters and 1 white counter are in a bag. One is chosen. How many outcomes are there?6
4 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.Examples1. A fair normal die is rolled, find the probability that a 5 occurs.
5 Question set 11. 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.
6 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.ColourSilverBlueBlackOtherFrequency2012135Another 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,
7 Complementary probabilities All probabilities must add up to 1.Questions4 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.
8 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,123456789101112a) a 2,b) a 7,c) a 10,This is the main body of the table, showing the 36 outcomes.d) a 1.
9 Question set 2Two 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.123456e) a non-prime number,f) not a 3.
10 ExpectationExpectation 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?ExamplesIf 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?