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PROBABILITY BY SHUBHAM

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PROBABILITY

PROBABILITY

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  • 1. Probability Probability
  • 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?
    • Probability is a number from 0 to 1 that tells you how likely something is to happen.
    • Probability can have two approaches -experimental 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 TO PROBABILITY
    • EXPERIMENT : An operation which can produce some well defines outcomes is called an experiment. Each outcome is called an event
    • RANDOM EXPERIMENT : An experiment in which all possible outcomes are known and the exact outcome cannot be predicted in advance , is called a random experiment
    • TRIAL : By a trial, we mean performing a random experiment.
    • EVENTS : The happenings of the desired occurrences are
    • Known as events.
  • 7. SOME TYPE OF EVENTS AND ITS PROBABILITY
    • IMPOSSIBLE EVENT AND ITS PROBABILITY
    • When no outcome favours an event out of all possible outcomes of a random experiment, the event is called an impossible event. The Probability of an impossible event is zero. e.g., in a single throw of dice, getting a number more than 6 is an impossible event.
  • 8. SURE OR CERTAIN EVENT AND ITS PROBABILITY
    • When all the outcomes favours an event, the event is called a sure event or certain event and the probability of a sure event or certain event is One e.g., in a single throw of dice, getting a number less than or equal to 6 is a sure event or certain event.
  • 9. EQUALLY LIKELY EVENTS
    • Two events are said to be equally likely, if the different outcomes have equal chances of occurrence i.e., there is no reason to expect an outcome in preference the other e.g., in getting a single toss of a coin, getting Head and getting Tail is equally likely.
  • 10. MUTUALLY 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.Theoretical
    • Experimental probability:
    • P(event) = number of times event occurs
    • total number of trials
    • Theoretical probability:
    • P(E) = number of favorable outcomes total number of possible outcomes
  • 12. How can you tell which is experimental and which is theoretical probability?
    • Experimental:
    • You tossed a coin 10 times and recorded a head 3 times, a tail 7 times
    • P(head)= 3/10
    • P(tail) = 7/10
    • Theoretical:
    • Toss a coin and getting a head or a tail is 1/2.
    • P(head) = 1/2
    • P(tail) = 1/2
  • 13. Experimental probability
    • Experimental probability is found by repeating an experiment and observing the outcomes .
    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 probability
    • P(head) = 1/2
    • P(tail) = 1/2
    • Since there are only two outcomes, you have 50/50 chance to get a head or a 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 the marble out of the bag, record colour. After 6 draws, you record 2 red marbles
    • P(red)= 2/6 = 1/3
    • Experimental
    • ( The result is found by repeating an 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 Review
    • Probability as a measure of likelihood
    • There are two types of probability
    • Theoretical--- theoretical measurement and can be found without experiment
    • Experimental--- measurement of a actual experiment and can be found by recording experiment outcomes
  • 19.