Probability space tables summary notes with worked examples

Probability
 Basic Probability questions
 Possibility space tables
Consider the following examples.
Example 1
There are 10 numbers in a lottery, numbers from 1 to 10.
Mr. Borg played number 6.
1
What are his chances of winning? Answer =
10
There is a total of 10 numbers and only one number 6.
1
b) What is the chance of getting 10 in this lottery? Answer =
10
2
c) Mr. Herd played 6 and 8. What are his chances of winning? Answer =
10
d) What is the chance of getting an odd number?
5
Answer is
10
9
e) Mr. Borg played the number 4. What are the chance of losing? Answer =
10


Example 2
A bag contains 3 yellow, 4 red and 5 green marbles.
4 1
a) What is the probability (chance) of picking a red marble? Answer = = (simplify the
12 3
fractions)
Note: we do the number of red marbles over the total amount of marbles. The total amount of
marbles is found by adding the total marbles.
In probability give your answer as a fraction.
4+ 5 9 3
b) What is the probability of getting a green or a red marble? Answer = = =
12 12 4



1

, Example 3


Ex3.) In a lottery there are the following numbers: 1, 4, 5, 6, 8, 10
a) What is the probability of getting a prime number? Note: 1 is not a prime number, 1 is a
square number. The only prime number is 5.
1
Answer =
6
2 1
b) what is the probability of getting a square number? Answer = =
6 3
Note: prime number: 2, 3, 5, 7, 11, 13…
Square numbers: 1, 4, 9, 16, 25, 36…
c) What is the probability of getting a number which is even and square as well?
1
Answer = ( 4 is the only number from the given set which is even and square at the same
6
time)




2