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