Probability
How to find the probability P(A): formula, 3 examples, and their solutions.
Formula
Formula
P(A) = n(A)/S(A)
P(A): Probability of an event A happening
n(A): Number of ways of an event A happening
n(S): Total number of ways
P is between 0 and 1.
P(A) = 0: Event A doesn't happen.
P(A) = 1: Event A always happens.
Example 1
Example
Solution
Set A as
getting a multiple of 3 from a fair die.
{3, 6}
The number of {3, 6} is 2.
So n(A) = 2.
A die has 6 sides.
So n(S) = 6.
Then P(A) = 2/6.
2/6 = 1/3
So 1/3 is the answer.
Example 2
Example
Solution
There are 3 blue marbles.
Then n(A) = 3.
(Set A as picking a blue marble.)
There are 3, 4, and 5 marbles in the jar.
So n(S) = 3 + 4 + 5.
3 + 4 = 7
7 + 5 = 12
So n(S) = 12.
There are 3 blue marbles.
So n(A) = 3.
There are 12 marbles in the jar.
So n(S) = 12.
Then P(A) = 3/12.
3/12 = 1/4
So 1/4 is the answer.
Example 3
Example
Solution
P(X ≥ 4) means
the probability of
getting a number greater than 4.
So it means
the probability of getting 4 or 5.
4 and 5 area is the colored area.
The colored area is 2/5 of the whole spinner.
So the probability of getting 4 or 5 is
2/5.
So 2/5 is the answer.