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Problems3

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  • 1. Problems Probability-3
  • 2. :3/4 Probability:   {yellow, blue, green, red} Sample Space:   A spinner has 4 equal sectors colored yellow, blue, green and red. What is the probability of landing on a sector that is not red after spinning this spinner? Question No 1
  • 3. Question No 2:
    • Experiment 2:   A single card is chosen at random from a standard deck of 52 playing cards. What is the probability of choosing a card that is not a king?
    • 12/13
  • 4. Question no 3
    •    A single 6-sided die is rolled. What is the probability of rolling a number that is not 4?
    • 5/6
  • 5. Question No 4
    • A single card is chosen at random from a standard deck of 52 playing cards. What is the probability of choosing a card that is a club?
    • 13/52
  • 6. Question no 5
    • A coin is tossed and a single 6-sided die is rolled. Find the probability of landing on the head side of the coin and rolling a 3 on the die
    • 1/12
  • 7. Question no 6
    • A card is chosen at random from a deck of 52 cards. It is then replaced and a second card is chosen. What is the probability of choosing a jack and an eight?
    •    1  
    • 169
      
  • 8. Addition Rule
    • The addition rule is a result used to determine the probability that event A or event B occurs or both occur.
    • Non mutually exclusive
    • The result is often written as follows, using set notation:
    • Where P(A) = probability that event A occurs
    • P(B) = probability that event B occurs
    • = probability that event A or event B occurs
    • = probability that event A and event B both occur
    • For mutually exclusive events , that is events which cannot occur together:
    • = 0
  • 9. Addition Rule Contd….
    • The addition rule therefore reduces to
    • = P(A) + P(B)
    • For independent events , that is events which have no influence on each other
    The addition rule therefore reduces to
  • 10. Multiplication Rule
    • The multiplication rule is a result used to determine the probability that two events, A and B, both occur.
    • The multiplication rule follows from the definition of conditional probability.
    • The result is often written as follows, using set notation:
    • where: P(A) = probability that event A occurs
    • P(B) = probability that event B occurs
    • = probability that event A and event B occur
    • P(A | B) = the conditional probability that event A occurs given that event B has occurred already
    • P(B | A) = the conditional probability that event B occurs given that event A has occurred already
    • For independent events, that is events which have no influence on one another, the rule simplifies to
    • :That is, the probability of the joint events A and B is equal to the product of the individual probabilities for the two events.
  • 11.
    • Statistical Independence
    • When the occurrence of one event does not affect and is not affected by the probability of occurrence of any other event
    • Probabilities under statistical independence –
    • Marginal Probability
    • Joint probability
    • Conditional Probability
  • 12. Marginal Probability
    • Refers one and only one event
  • 13. Joint Probability
    • The Probability of two or more independent events occur together or in succession is called joint probability
    • P(AB)=P(A  B)=P(A)*P(B)
  • 14. Conditional Probability
    • For statistically independent events A and B the conditional probability denoted by P(A/B) of event A given that B has already occurred is simply the probability of event A
    • P(A/B)=P(A)
    • Like that
    • P(B/A)=P(B)
  • 15. Statistical Dependence events
    • Marginal Probability
    • Same like statistical Independence
    • P(A)= P(A  B)+ P(A  B)
    • P(B)= P(A  B)+ P(A  B)
  • 16. Joint Probability
    • Dependent Events
    • P(A and B) ≠P (A  B) ≠ P(A  )*P(B)
    • P(A) ≠ P(A/B) and P(B) ≠ P(B/A)
    • The Probability of two or more dependent events occur together or in succession is called joint probability
    • P(A  B)=P(A)*P(B/A)
    • P(A  B)=P(B)*P(A/B)
  • 17. Conditional Probability
    • P(A  B)
    • P(A/B) =
    • P(B)
    • Gives Conditional Probability of B given that the event A has occurred
  • 18. Baye’s Theorem
    • Suppose an event has happened as a result of several causes . Then we are interested to find out the probability of a particular cause which really affected the event to happen. Problems of this type are called inverse probability . Baye’s theorem is based on inverse probability

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