How to Find a Probability
Question
What is the probability of getting Heads in a coin toss?
Step-by-Step:
1
Find the number of ways getting Heads can happen.
There is only 1 way of getting Heads.
There is only 1 way of getting Heads.
2
Find the total number of outcomes.
There are 2 outomes: getting Heads and getting Tails.
There are 2 outomes: getting Heads and getting Tails.
3
Divide the number of ways of getting Heads (1) (found in Step 1) by the total number of outcomes (2) (found in Step 2).
Probability of getting heads = 1 ÷ 2 = 0.5
Answer:
The probability of getting Heads is 0.5. Using notation, if H is the event of a Heads coming up, the probability of the event is P(H).
We can also express this as a fraction (½) or a percentage (50%).
A Formula to Find a Probability
The formula for finding a probability is shown below:
$$Probability = \frac{Number~of~ways~an~event~can~happen}{Total~number~of~outcomes}$$
Let's use the formula in an example.
Question
What is the probability of rolling a 6 on a die?
Step-by-Step:
1
Start with the formula.
$$Probability = \frac{Number~of~ways~an~event~can~happen}{Total~number~of~outcomes}$$
2
Find the number of ways the event can happen.
Find the number of ways getting a 1 can happen.
There is only 1 way of rolling a 1.
There is only 1 way of rolling a 1.
3
Find the total number of outcomes.
There are 6 outomes: getting 1, 2, 3, 4, 5 and 6.
There are 6 outomes: getting 1, 2, 3, 4, 5 and 6.
4
Substitute the number of ways the event can happen and the total number of outcomes into the formula.
$$Probability = \frac{1}{6}$$
Answer:
The probability of rolling a 1 is 1⁄6. Using notation, if 1 is the event of rolling a 1, the probability of the event is P(1).
We can also express this as a number (0.167) or a percentage (16.7%).
A Note on Notation
The probability of an event can be written as:
P(Event)
A letter or symbol can be used to represent an event.
For example, let H be the event that a coin lands on Heads when it has been tossed.
We can denote the probability of getting heads as:
P(H)
This page was written by Stephen Clarke.
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