Download presentation

1
**Probability 1: the idea of probability**

IB Studies Adrian 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
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

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. Examples 1. A fair normal die is rolled, find the probability that a 5 occurs.

5
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.

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. 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,

7
**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.

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, 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.

9
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.

10
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?

11
Question set 3

Similar presentations

Presentation is loading. Please wait....

OK

Theoretical Probability

Theoretical Probability

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google