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PROBABILITY
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ProbabilityProbability
ProbabilityProbability
POWER POINT PRESENTATION
PROBABILITYGROUP MEMBERS
SOURABH AND SHAILENDRA { GROUP LEADERS}SHUBHAMRAVINDERRISHABHSANGAM
SHASHANAK SHEKHAR
POWER POINT PRESENTATIONGroup membersSOURABHSHEILENDRASHUBHAMSANGAM SHASHANKSHEKHARRAVINDERRISHABH
Objectives
To Explore Probability
To explore experimental and theoretical
probability with experiments and simulations
To calculate and compare both probabilities
What do you know about probability?What do you know about probability?
Probability is a number from 0 to 1 Probability is a number from 0 to 1 that tells you how likely something is that tells you how likely something is to happen.to happen.
Probability can have two approaches Probability can have two approaches -experimental probability-experimental probability
-theoretical probability-theoretical probability
Key Words
• Experimental probability• Theoretical probability• Outcome• Event• Random EXPERIMENT• SAMPLE SPACE
• IMPOSSIBLE EVENTS AND ITS PROBABILITY
• SURE OR CERTAIN EVENT AND ITS PROBABILITYEQUAALLY LIKELY EVENTS• MUTUALLY EXCLUSIVE EVENTS
SOME TERMS RELATED TO SOME TERMS RELATED TO PROBABILITYPROBABILITY
EXPERIMENT : An operation which can produce some well EXPERIMENT : An operation which can produce some well defines outcomes is called an experiment. Each outcome defines outcomes is called an experiment. Each outcome is called an eventis called an event
RANDOM EXPERIMENT : An experiment in which all RANDOM EXPERIMENT : An experiment in which all possible outcomes are known and the exact outcome possible outcomes are known and the exact outcome cannot be predicted in advance , is called a random cannot be predicted in advance , is called a random experimentexperiment
TRIAL : By a trial, we mean performing a random TRIAL : By a trial, we mean performing a random experiment.experiment.
EVENTS : The happenings of the desired occurrences are EVENTS : The happenings of the desired occurrences are Known as events.Known as events.
SOME TYPE OF EVENTS AND SOME TYPE OF EVENTS AND ITS PROBABILITYITS PROBABILITY
• IMPOSSIBLE EVENT AND ITS IMPOSSIBLE EVENT AND ITS PROBABILITYPROBABILITY
• When no outcome favours an When no outcome favours an event out of all possible outcomes event out of all possible outcomes of a random experiment, the event of a random experiment, the event is called an impossible event. The is called an impossible event. The Probability of an impossible event Probability of an impossible event is zero. e.g., in a single throw of is zero. e.g., in a single throw of dice, getting a number more than dice, getting a number more than 6 is an impossible event.6 is an impossible event.
SURE OR CERTAIN EVENT SURE OR CERTAIN EVENT AND ITS PROBABILITYAND ITS PROBABILITY
When all the outcomes favours an When all the outcomes favours an event, the event is called a sure event, the event is called a sure event or certain event and the event or certain event and the probability of a sure event or certain probability of a sure event or certain event is One e.g., in a single throw event is One e.g., in a single throw of dice, getting a number less than of dice, getting a number less than or equal to 6 is a sure event or or equal to 6 is a sure event or certain event.certain event.
EQUALLY LIKELY EVENTSEQUALLY LIKELY EVENTS
Two events are said to be equally Two events are said to be equally likely, if the different outcomes have likely, if the different outcomes have equal chances of occurrence i.e., equal chances of occurrence i.e., there is no reason to expect an there 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 is getting Head and getting Tail is equally likely.equally likely.
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
Experimental vs.TheoreticalExperimental vs.Theoretical
Experimental probability:Experimental probability:
P(event) = P(event) = number of times event number of times event occursoccurs
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 total number of possible
outcomesoutcomes
How can you tell which is experimental How can you tell which is experimental and which is theoretical probability?and which is theoretical probability?
Experimental:Experimental:
You tossed a coin 10 You tossed a coin 10 times and recorded a times and recorded a head 3 times, a tail 7 head 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 getting Toss a coin and getting a head or a tail is a head or a tail is 1/2.1/2.
P(head) = 1/2P(head) = 1/2
P(tail) = 1/2P(tail) = 1/2
Experimental probabilityExperimental probability
Experimental probability is found by Experimental probability is found by repeating an repeating an experimentexperiment and observing the and 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
Theoretical probabilityTheoretical probabilityP(head) = 1/2P(head) = 1/2P(tail) = 1/2P(tail) = 1/2Since there are Since there are
only two only two outcomes, you outcomes, you have 50/50 have 50/50 chance to get a chance to get a head or a tail. head or a tail.
HEADS
TAILS
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)
You draw a marble, and replace the You draw a marble, and replace the marble out of the bag, record colour. marble out of the bag, record colour.
After 6 draws, you record 2 red After 6 draws, you record 2 red marblesmarbles
P(red)= 2/6 = 1/3P(red)= 2/6 = 1/3 ExperimentalExperimental
((The result is found by repeating an The result is found by repeating an experiment.)experiment.)
Contrast Experimental and theoretical
probability Experimental probability is the
result of an experiment.
Theoretical probability is what is expected to happen.
Lesson ReviewLesson Review
Probability as a measure of Probability as a measure of likelihoodlikelihood
There are two types of probabilityThere are two types of probability Theoretical--- theoretical Theoretical--- theoretical
measurement and can be found measurement and can be found without experimentwithout experiment
Experimental--- measurement of a Experimental--- measurement of a actual experiment and can be found actual experiment and can be found by recording experiment outcomesby recording experiment outcomes