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# PROBABILITY BY SHUBHAM

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PROBABILITY

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### PROBABILITY BY SHUBHAM

1. 1. ProbabilityProbability ProbabilityProbability
2. 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. 3. Objectives To Explore Probability To explore experimental and theoretical probability with experiments and simulations To calculate and compare both probabilities
4. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 17. Contrast Experimental and theoretical probability Experimental probability is the result of an experiment. Theoretical probability is what is expected to happen.
18. 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