Probability
How to find the probability of an event: definition, examples, and their solutions.
Definition
The probability of an event can be found
by using the formula below.
P(A) = n(A)/n(S)
P(A): Probability of the event A happening
n(A): Number of ways of the event A happening
n(S): Total number of ways
(= Number of space sample)
S stands for the [sample space].
The probability has a value between 0 and 1.
P(A) = 0 means
the event A doesn't happen.
P(A) = 1 means
the event A always happens.
So 0 ≤ P(A) ≤ 1.
Example 1
A die has 6 sides: from 1 to 6.
So there are 6 ways to get a number.
So n(S) = 6.
Set the event A as getting a 3.
There's 1 way to get a 3.
So n(A) = 1.
n(S) = 6
n(A) = 1
So the probability of getting a 3 is
P(A) = 1/6.
Example 2
A die has 6 sides: from 1 to 6.
So there are 6 ways to get a number.
So n(S) = 6.
Set the event A as
getting an odd number.
The odd numbers from 1 to 6 are
{1, 3, 5}.
There are 3 ways
to get an odd number.
So n(A) = 3.
n(S) = 6
n(A) = 3
So the probability of getting an odd number is
P(A) = 3/6.
Divide the numerator and the denominator by 3.
Then 3/6 = 1/2.
Example 3
Numbers from 1 to 30 are given.
So there are 30 numbers
that can be picked.
So n(S) = 30.
Set the event A as
picking a prime number.
The prime numbers from 1 and 30 are
{2, 3, 5, 7, 11, 13, 17, 19, 23, 29}.
There are 10 prime numbers
that can be picked.
So n(A) = 10.
n(S) = 30
n(A) = 10
So P(A) = 10/30.
Divide the numerator and the denominator by 10.
Then 10/30 = 1/3.
Example 4
The spinner is divided into five parts:
from 1 to 5.
And each part has the same area.
So there are 5 ways
that the arrow can land.
So n(S) = 5.
[X = 2] means
the event of landing at 2.
There's only 1 way
that the arrow can land at 2.
So n(A) = 1.
n(S) = 5
n(X = 2) = 1
So P(X = 2) = 1/5.
Example 5
The pizza is divided into 8 pieces.
So n(S) = 8.
Set the event A as
choosing the piece with pepperoni.
There are 5 pieces
that have pepperoni on them.
So n(A) = 5.
n(S) = 8
n(A) = 5
So P(A) = 5/8.
