PROBABILITY

1. ProbabilityProbability
ProbabilityProbability

2. POWER POINT
PRESENTATION
PROBABILITY
GROUP MEMBERS
SOURABH AND SHAILENDRA { GROUP LEADERS}
SHUBHAM
RAVINDER
RISHABH
SANGAM
SHASHANAK
SHEKHAR
POWER POINT
PRESENTATION
Group members
SOURABH
SHEILENDRA
SHUBHAM
SANGAM
SHASHANK
SHEKHAR
RAVINDER
RISHABH

3. Objectives
To Explore Probability
To explore experimental and theoretical
probability with experiments and simulations
To calculate and compare both probabilities

4. What do you know about probability?What do you know about probability?
 Probability is a number from 0 to 1 thatProbability is a number from 0 to 1 that
tells you how likely something is totells you how likely something is to
happen.happen.
 Probability can have two approachesProbability can have two approaches
-experimental probability-experimental probability
-theoretical probability-theoretical probability

5. Key Words
• Experimental probability
• Theoretical probability
• Outcome
• Event
• Random EXPERIMENT
• SAMPLE SPACE
• IMPOSSIBLE EVENTS AND ITS PROBABILITY
• SURE OR CERTAIN EVENT AND ITS PROBABILITY
EQUAALLY LIKELY EVENTS
• MUTUALLY EXCLUSIVE EVENTS

6. SOME TERMS RELATED TOSOME TERMS RELATED TO
PROBABILITYPROBABILITY
 EXPERIMENT : An operation which can produce someEXPERIMENT : An operation which can produce some
well defines outcomes is called an experiment. Eachwell defines outcomes is called an experiment. Each
outcome is called an eventoutcome is called an event
 RANDOM EXPERIMENT : An experiment in which allRANDOM EXPERIMENT : An experiment in which all
possible outcomes are known and the exact outcomepossible outcomes are known and the exact outcome
cannot be predicted in advance , is called a randomcannot be predicted in advance , is called a random
experimentexperiment
 TRIAL : By a trial, we mean performing a randomTRIAL : By a trial, we mean performing a random
experiment.experiment.
 EVENTS : The happenings of the desired occurrencesEVENTS : The happenings of the desired occurrences
areare

7. SOME TYPE OF EVENTS ANDSOME TYPE OF EVENTS AND
ITS PROBABILITYITS PROBABILITY
• IMPOSSIBLE EVENT AND ITSIMPOSSIBLE EVENT AND ITS
PROBABILITYPROBABILITY
• When no outcome favours an event outWhen no outcome favours an event out
of all possible outcomes of a randomof all possible outcomes of a random
experiment, the event is called anexperiment, the event is called an
impossible event. The Probability of animpossible event. The Probability of an
impossible event is zero. e.g., in aimpossible event is zero. e.g., in a
single throw of dice, getting a numbersingle throw of dice, getting a number
more than 6 is an impossible event.more than 6 is an impossible event.

8. SURE OR CERTAIN EVENT ANDSURE OR CERTAIN EVENT AND
ITS PROBABILITYITS PROBABILITY
 When all the outcomes favours an event, theWhen all the outcomes favours an event, the
event is called a sure event or certain event andevent is called a sure event or certain event and
the probability of a sure event or certain event isthe probability of a sure event or certain event is
One e.g., in a single throw of dice, getting aOne e.g., in a single throw of dice, getting a
number less than or equal to 6 is a sure event ornumber less than or equal to 6 is a sure event or
certain event.certain event.

9. EQUALLY LIKELY EVENTSEQUALLY LIKELY EVENTS
 Two events are said to be equallyTwo events are said to be equally
likely, if the different outcomes havelikely, if the different outcomes have
equal chances of occurrence i.e.,equal chances of occurrence i.e.,
there is no reason to expect anthere is no reason to expect an
outcome in preference the other e.g.,outcome in preference the other e.g.,
in getting a single toss of a coin,in getting a single toss of a coin,
getting Head and getting Tail isgetting Head and getting Tail is
equally likely.equally likely.

10. MUTUALLY EXCLUSIVE EVENTSMUTUALLY EXCLUSIVE EVENTS
• Two events in a random experiment are
said to be mutually exclusive, if they
cannot occur together. e.g., in a single
throw of coin, getting head or getting tail
together is not possible

11. Experimental vs.TheoreticalExperimental vs.Theoretical
Experimental probability:Experimental probability:
P(event) =P(event) = number of times event occursnumber of times event occurs
total number of trialstotal number of trials
Theoretical probability:Theoretical probability:
P(E) =P(E) = number of favorable outcomesnumber of favorable outcomes
total number of possible outcomestotal number of possible outcomes

12. How can you tell which isHow can you tell which is
experimental and which isexperimental and which is
theoretical probability?theoretical probability?
Experimental:Experimental:
You tossed a coin 10You tossed a coin 10
times and recorded atimes and recorded a
head 3 times, a tail 7head 3 times, a tail 7
timestimes
P(head)= 3/10P(head)= 3/10
P(tail) = 7/10P(tail) = 7/10
Theoretical:Theoretical:
Toss a coin and gettingToss a coin and getting
a head or a tail isa head or a tail is
1/2.1/2.
P(head) = 1/2P(head) = 1/2
P(tail) = 1/2P(tail) = 1/2

13. Experimental probabilityExperimental probability
Experimental probability is found byExperimental probability is found by
repeating anrepeating an experimentexperiment and observing theand observing the
outcomesoutcomes..
P(head)= 3/10
A head shows up 3 times out of 10 trials,
P(tail) = 7/10
A tail shows up 7 times out of 10 trials

14. Theoretical probabilityTheoretical probability
P(head) = 1/2P(head) = 1/2
P(tail) = 1/2P(tail) = 1/2
Since there are onlySince there are only
two outcomes, youtwo outcomes, you
have 50/50 chancehave 50/50 chance
to get a head or ato get a head or a
tail.tail.
HEADS
TAILS

15. Identifying the Type of Probability
A bag contains three
red marbles and three
blue marbles.
P(red) = 3/6 =1/2
 Theoretical
(The result is based on the
possible outcomes)

16. You draw a marble, and replace theYou draw a marble, and replace the
marble out of the bag, record colour. Aftermarble out of the bag, record colour. After
6 draws, you record 2 red marbles6 draws, you record 2 red marbles
P(red)= 2/6 = 1/3P(red)= 2/6 = 1/3
 ExperimentalExperimental
((The result is found by repeating anThe result is found by repeating an
experiment.)experiment.)

17. Contrast Experimental
and theoretical
probability
Experimental probability is the
result of an experiment.
Theoretical probability is what is
expected to happen.

18. Lesson ReviewLesson Review
 Probability as a measure ofProbability as a measure of
likelihoodlikelihood
 There are two types of probabilityThere are two types of probability
 Theoretical--- theoreticalTheoretical--- theoretical
measurement and can be foundmeasurement and can be found
without experimentwithout experiment
 Experimental--- measurement of aExperimental--- measurement of a
actual experiment and can be foundactual experiment and can be found
by recording experiment outcomesby recording experiment outcomes