Basic concepts of probability

1. Concept of Probability
and important terms,
Independent events
and Conditional
probability

2. Introduction
Probability is a branch of mathematics
that deals with the likelihood of events
occurring. It helps us make sense of
uncertainty and randomness in various
situations. In this presentation, we will
explore the fundamental concepts of
probability, including important terms,
independent events, and conditional
probability.

3. Important Terms
Probability
The likelihood of an event
happening, usually expressed as a
number between 0 and 1.
Sample Space
The set of all possible outcomes of
an experiment.
Event
The set of all possible outcomes of
an experiment.

4. Independent
Events
Independent events are events
where the outcome of one event
does not affect the outcome of
another event.
Formula:
P(A∩B)=P(A)×P(B)

5. Independent Events:
Independent events are events where the outcome of one event does not affect the outcome of
another event. In simpler terms, the occurrence of one event does not influence the probability of
the other event happening. For example, flipping a coin twice or rolling a die multiple times are
independent events because the outcome of the first flip or roll does not change the outcome of
the subsequent flips or rolls. Each event is unaffected by the other, and their probabilities remain
the same regardless of the outcomes of other events.

6. Suppose you have abag containing 4 red marbles and 3 blue marbles. If you draw two
marbles from the bag without replacement, what is the probability of drawing ared marble
followed by ablue marble?
Probability of drawing a red marble on the
first draw:
There are 4 red marbles out of a total of 7
marbles in the bag.
So, the probability of drawing a red marble
on the first draw is 4/7. Since we didn't replace the first marble, now
there are 3 red marbles and 6 marbles in
total. The probability of drawing a blue
marble now is 3/6, which simplifies to 1/2.
Multiplying the probabilities of both
events:Probability of drawing a red
marble followed by a blue marble =
(4/7) * (3/6) = 2/7.

7. Conditional
Probability
Conditional probability is the
probability of an event occurring
given that another event has
already occurred.
Using the formula for conditional probability: P(S|M) = P(S and
M) / P(M), we can calculate
1. Probability of passing both tests (P(S and M)) = P(S|M) * P(M) = 0.80 *
0.60 = 0.48.
2.Now, to find P(S|M), we divide the probability of passing both tests by
the probability of passing the math test: P(S|M) = 0.48 / 0.60 = 0.8.
Problem
Suppose a group of students took a math and a science test. Out of
the students who passed the math test, 80% also passed the science
test. If 60% of all students passed the math test and 70% passed the
science test, what is the probability that a student who passed the
math test also passed the science test?
solution:
We are given the following probabilities:
Probability of passing the math test (P(M)) = 0.60
Probability of passing the science test (P(S)) = 0.70
Probability of passing the science test given that the math test was passed (P(S|M)) = 0.80
P(A|B)=P(A∩B)/P(B)
Formula:

8. Conditional probability is a measure of the likelihood of an event occurring, given that another
event has already occurred. In simpler terms, it's the probability of one event happening, based on
the occurrence of another event.
For example, let's say you're playing a card game, and you want to know the probability of drawing
a red card from a deck of cards, given that you've already drawn a face card. The probability of
drawing a red card (event A) changes based on the condition that you've already drawn a face
card (event B).
Conditional probability

9. Real-Life Applications:
Weather Forecasting
Meteorologists use probability to predict the
likelihood of rain, snow, or other weather
conditions.
By analyzing past weather patterns and current
atmospheric conditions, they calculate the
probability of specific weather events occurring.

10. Real-Life Applications:
Medical Diagnosis
Doctors use probability to
assess the likelihood of a
patient having a certain
disease based on symptoms,
test results, and risk factors.
This helps them make
informed decisions about
treatment and management
strategies.

11. Real-Life Applications:
Financial Planning
Investors use probability to assess the
risk and potential return of various
investment options.
By calculating probabilities of
different market outcomes, they can
make more informed investment
decisions to achieve their financial
goals.

12. Thank You
Probability and Important terms done by 2305842
Independent Events done by 2305843
Conditional Probability done by 2305836