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# Problems3

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### Transcript

• 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

• 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
• 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