This presentation includes the definitions and properties of basic terms in Probability.

1. PROBABILITY DEFINITIONS AND
PROPERTIES
BY:
Razi Ali Valliani 2012222
Shan Virani 2012228
Hamza Qureshi 2012214
Ritick Kumar 2012224

2. Whatisprobability?
 Probability is the way of expressing knowledge of belief
that an event will occur in chance.
 Probability is the measure of how likely it is the some
event will occur, a number expressing the ratio of favorable
cases to the whole number or cases possible.
 Formula: no.of favorable outcomes/Total no.of events
What is
probability?

3. Example
 Consider the example of finding the probability of
selecting a black card or a 6 from a deck of 52 cards.
Solution:
We need to find out P(B or 6)
Probability of selecting a black card = 26/52
Probability of selecting a 6 = 4/52
Probability of selecting both a black card and a 6 = 2/52
P(B or 6) = P(B) + P(6) – P(B and 6)
= 26/52 + 4/52 – 2/52
= 28/52= 7/13.

4. Whereis
probability
used?
 Probability is used a lot in daily life.
 Probability is used in such as math, statistics, Finance,
Gambling, Science, Machines and artificial intelligence, and
in many other activities.

5. How dowe
express
probabilities?
 Mostly, we express probabilities as fractions.
 The numerator shows possible number of ways an event can occur.
 The denominator is a total number of possible event that could occur.

6. Somecommon
termsrelatedto
probability.
 Experiment: Is a situation involving chance or probability that
leads to results called outcomes.
 Outcome: A possible result of a random experiment.
 Sample space: The set of outcomes of an experiment is known
as sample space.
 Event: One or more outcomes in an experiment.
 Sample point: Each element of sample space is called a sample
point.

7. Generalrulesof
probability.
 Probability is a number between 0 and 1.
 The sum of probabilities of all possible outcomes in a sample
space is 1.
 The probability that an event does not occur is 1 minus the
probability that it does occur.(also called component of A).

8. Independent
Events
 Two events are independent if outcome of event A, has
no effect on outcome of event B.
 When multiple events occur, if the outcome of one
event DOES NOT affect the outcome of the other
events, they are called independent events.
For Example: Say, a die is rolled twice. The outcome of
the first roll doesn’t affect the second outcome. These two
are independent events.

9. Example1
Example 1:
Say, a coin is tossed twice. What is the probability of
getting two consecutive tails ?
Probability of getting a tail in one toss = ½
The coin is tossed twice. So 1/2 * 1/2 = 1/4 is the answer.
Here’s the verification of the above answer with the help
of sample space.
When a coin is tossed twice, the sample space is {(H,H),
(H,T), (T,H), (T,T)}.
Our desired event is (T,T) whose occurrence is only once
out of four possible outcomes and hence, our answer is
1/4.

10.  Example 2: Consider another example where a pack
contains 4 blue, 2 red and 3 black pens. If a pen is
drawn at random from the pack, replaced and the
process repeated 2 more times, What is the probability
of drawing 2 blue pens and 1 black pen ?
 Solution
 Here, total number of pens = 9
 Probability of drawing 1 blue pen = 4/9
 Probability of drawing another blue pen = 4/9
 Probability of drawing 1 black pen = 3/9
 Probability of drawing 2 blue pens and 1 black pen =
4/9 * 4/9 * 3/9 = 48/729 = 16/243
Example 2

11. Conditional
probability
 The conditional probability of an event A is the probability that
an event A will occur given that another event, B, has occurred.
 Formula: probability(A|B)=P(AnB)/P(B).

12. Example
 In a class, 40% of the students study math and
science. 60% of the students study math. What is the
probability of a student studying science given he/she
is already studying math ?
 Solution
 P(M and S) = 0.40
 P(M) = 0.60
 P(S|M) = P(M and S)/P(S) = 0.40/0.60 = 2/3 = 0.67

13. Experimental
probability
 An experimental probability is one that happens as the result of
an experiment.
 Formula: (# of outcomes)/(# of trials)
 Example: Weather Forecasting. Before planning for an outing
or a picnic, we always check the weather forecast. ...