2. Probability and Chance
3. What Is Probability?
Probability is a measure of how likely it is for an event to
happen.
We name a probability with a number from 0 to 1.
If an event is certain to happen, then the probability of the event
is 1.
If an event is certain not to happen, then the probability of the
event is 0.
We can even express probability in percentage.
4. Chance
Chance is how likely it is that something will
happen. To state a chance, we use a percent.
Certain not to happen ---------------------------0%
Equally likely to happen or not to happen ----- 50 %
Certain to happen ----------------------------------- 100%
5. Examples Of Chance
6. Donald is rolling a number cube labeled 1 to 6. Which of the
following is LEAST LIKELY? an even number
an odd number
a number greater than5
7. The History of Probability
Probability originated from the study of games of chance. Tossing a
dice or spinning a roulette wheel are examples of deliberate
randomization that are similar to random sampling. Games of chance
were not studied by mathematicians until the sixteenth and
seventeenth centuries. Probability theory as a branch of
mathematics arose in the seventeenth century when French gamblers
asked Blaise Pascal and Pierre de Fermat (both well known pioneers
in mathematics) for help in their gambling. In the eighteenth and
nineteenth centuries, careful measurements in astronomy and
surveying led to further advances in probability.
8. Modern Use Of Probability
In the twentieth century probability is used to control the flow of
traffic through a highway system, a telephone interchange, or a
computer processor; find the genetic makeup of individuals or
populations; figure out the energy states of subatomic particles;
Estimate the spread of rumors; and predict the rate of return in
risky investments.
9. Predictable and Unpredictable Occurrence
Predictable Occurrences:The time an object takes to hit the ground
from a certain height can easily be predicted using simple physics.
The position of asteroids in three years from now can also be
predicted using advanced technology.Unpredictable Occurrences:Not
everything in life, however, can be predicted using science and
technology. For example, a toss of a coin may result in either a
head or a tail. Also, the sex of a new-born baby may turn out to be
male or female. In these cases, the individual outcomes are
uncertain. With experience and enough repetition, however, a
regular pattern of outcomes can be seen (by which certain
predictions can be made).
10. Formulae Of Probability
Ans. Let Ei denote the event of getting outcome i where
i=1,2,3,4,5,6:-
Then;Probability of outcome 1=Frequency of 1
Total no. of outcomes
=1791000
=0.179
Therefore, the sum of all the probabilities , i.e, E1 + E2 + E3+
E4+ E5 + E6
is equal to 1.
11. To know the opinion of students for the subject maths, a survey
of 200 students was conducted :-
Find the probability for both the opinions :
Ans. Total no. of observations = 200
P(Likeness of the students) =No. of students who like
Total no. of students
=135 200
= 0.675
P(Dislikeness of the students) =65200
= 0.325
12. Random Phenomenon
An event or phenomenon is called random if individual outcomes are
uncertain but there is, however, a regular distribution of relative
frequencies in a large number of repetitions. For example, after
tossing a coin a significant number of times, it can be seen that
about half the time, the coin lands on the head side and about half
the time it lands on the tail side.
Note of interest: At around 1900, an English statistician named
Karl Pearson literally tossed a coin 24,000 times resulting in
12,012 heads thus having a relative frequency of 0.5005 (His
results were only 12 tosses off from being perfect!).
13. Applications
14. A significant application of probability theory in everyday life is reliability. Many consumer products, such as automobiles and consumer electronics, utilize reliability theory in the design of the product in order to reduce the probability of failure. The probability of failure may be closely associated with the product's warranty.
Top Related