Probability and possibility are both used as nouns and can’t be used interchangeably. Although they have almost the same meanings, there is a little difference. Probability means something may happen, but it is more likely to happen. Meanwhile, possibility means something may happen, but we don’t know how likely. It describes the uncertainty of whether an event may or may not happen.
Therefore, probability has a higher chance that an event will likely happen, compared to possibility that’s uncertain whether something may happen or may not happen.
When to Use Probability
We use probability as a noun when referring to the chance that something will happen, and is sometimes calculated mathematically. It has two definitions. First, it means how likely something is. Second, it refers to the chance that a given event will occur and will probably happen.
Meaning to say, if something is probable, then it is likely to happen. Hence, the word probability is often used when talking about something that has a greater chance of happening.
The level of certainty of something happening
The probability of winning the raffle is very low.
There is a 90% probability that the operation will succeed without complications.
There is a high probability that her son will use a coarse language when talking to older people.
The chance that something will likely happen
The probability is that local businesses will benefit more from the new law.
Not resorting to violence is now a probability rather than a possibility.
Based on the studies, there’s a high probability that the virus can be transmitted
When to Use Possibility
We use possibility when referring to the capability of something happening. It describes an event that is either possible or not. There’s no certainty whether something will or will not happen. Another definition of possibility is it refers to an opportunity to do something or something that can be done.
A chance that something may happen
There is a possibility that it will rain in the afternoon.
Due to the company’s increased revenue, hiring more employees is now a possibility.
The doctors are considering the possibility that the disease may be curable.
An opportunity to do something
We need to check all the possibilities for helping less unfortunate people.
There could have been great possibilities when Segway scooters were still popular.
The rescuers will not stop until they exhaust all the possibilities of saving people.
Probability vs. Possibility: Which One Is Correct?
Probability and possibility are both correct and have similar meanings, but there is a slight difference. Probability means something may happen, but it is more likely to happen. On the other hand, possibility means something may happen, but the likelihood is not determined.
2. Possibilities and Probabilities
• A measure of the likelihood that an event in
the future will happen
• Example: In one soccer game, there are
three possibilities how the game will be
ended
3. Tree diagram
• A graph that is helpful in organizing
calculations that involve several stages.
• Example: In a medical study, patients are
classified according to whether they have
blood type A, B, AB, or O and also
according to whether their blood pressure is
low, normal, or high. In how many different
ways can a patient be classified according to
blood type and blood pressure?
4. Multiplication of Choices
• If a choices consists of two steps, of which
the first can be made in m ways and for
each of these the second can be made in n
ways, then whole choice can be made in
m.n ways
• Example: Use the Medical Study Example
5. Example
• An Internet clothing retailer offers sweaters
and socks for women. The sweaters and
socks are offered in coordinating colors, If
sweaters are available in five colors and the
socks are available in four colors, how
many different outfits can be advertised?
6. Permutations
A Permutation is any arrangement of r
objects selected from n possible objects.
Note: The order of arrangement is important in
permutations.
8. Example
There are 12 players on the
Carolina Forest High School
basketball team. Coach
Thompson must pick five
players among the twelve on
the team to comprise the
starting lineup. How many
different groups are possible?
(Order does not matter.)
9. Example
Suppose that in
addition to
selecting the
group, he must
also rank each of
the players in
that starting
lineup according
to their ability
(order matters).
10. Example
• In a lottery game, three numbers are
randomly selected from balls numbered 1
through 50.
a. How many permutations are possible?
b. How many combinations are possible?
11. The Classical Probability
Concept
• The oldest way of measuring uncertainty
• Originally, it was developed in connection with games of
chance
• Has a value range from 0 to 1.
• Expressed in : decimal, or percentage.
• Ex. A die is tossed once. The probability of getting an odd
number on the upper face of the die is ½, 0.5, or 50%
• If there are n equally likely possibilities, of which one must
occur and s are regarded as favorable, then the probability
of a success is s/n
12. Examples
• What is the probability of rolling a 2 with a
well-balanced die?
• A manufacturer of cell phones plans to ship 12 cell
phones to a customer and, as a precaution, orders 4
of the phones to be checked. The 4 phones were
checked and found to be satisfactory, in spite of
the fact that the 12 phone shipment contained 2
defectives. What is the probability that the 4
phones that were checked will contain no
defectives when, actually, 2 of the 12 phones are
defective?
13. The Frequency Interpretation of
Probability
• The probability of an event (happening or
outcome) is the proportion of the time that events
of the same kind will occur in the long run
• Example: If records show that 506 of 814
automatic dishwashers sold by a large retailer
required repairs within the warranty year, what is
the probability that an automatic dishwasher sold
by this retailer will not require repairs within the
warranty year?
14. Mathematical Expectation
• Rational or Logical thinking of possibilities
or probabilities might arise.
• In its simplest form it is the product of
the amount a player stands to win and the
probability that he or she will win
• Ex. What is our mathematical expectation if
we buy 1 of 2000 raffle tickets issued for a
television set worth $540?
15. Mathematical Expectation
(Cont’d)
• If the probabilities of obtaining the amounts a1
, a2
,
…, or ak
are, respectively, p1
, p2
, …, and pk
, then
the mathematical expectation is
E = a1
p1
+ a2
p2
+ …. + ak
pk
E = Σ a . p
• In so far as the a’s are concerned, it is important to
keep in mind that they are positive when they
represent profits, winnings, or gains (amount that
we receive) and that they are negative when they
represent losses, penalties, or deficits (amount that
we have to pay).
16. Example
• What is our mathematical expectation if we
win $6 when a die comes up 1 or 2 and lose
$3 when the die comes up 3, 4, 5, or 6?
17. Decision Problem
• In facing uncertainties, mathematical
expectations can be often used to great
advantage in making decision
• In general if we have to choose between two
or more alternatives, mathematical
expectations will help ask to choose the
most promising one, such as that maximizes
expected profits, minimizes expected costs,
and so forth
18. Example
• A clothing manufacturer must decide whether to spend a
considerable sum of money to build a new factory. He
knows that if the new factory is built and the clothing
business has a good sales year, there will be a $451,000
profit; if the new factory is built and the clothing business
has a poor sales year, there will be a deficit of $110,000; if
the new factory is not built and the clothing business has a
good year, there will be a $220,000 profit; and if the new
factory is not built and the clothing business has a poor
year, there will be a $22,000 profit (mostly because of
lower overhead cost). If the clothing manufacturer feels
that the probabilities for a good sales year or a poor sales
year are, respectively, 0.4 and 0.6, would building the new
factory maximize his expected profit?
