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Independent Events

Independent Events. Mutually Exclusive and Inclusive Events. These typically refer to single events (you are only making one selection) You need to make sure you are not double counting an overlapping scenario. Mutually Exclusive.

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Independent Events

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  1. Independent Events

  2. Mutually Exclusive and Inclusive Events • These typically refer to single events (you are only making one selection) • You need to make sure you are not double counting an overlapping scenario

  3. Mutually Exclusive • If two things are mutually exclusive, it means that they cannot happen at the same time. • Example: you cannot flip a coin and get both heads and tails or draw a card and get both a club and a red card. These events DO NOT overlap

  4. Mutually Inclusive • If two things are mutually inclusive, it means that they can happen at the same time. • Example: rolling a dice and getting an even number or a 4. • In this case, rolling the 4 is INCLUDED in the even number requirement. I should not double count the 4. These events DO overlap

  5. Example • What is the probability of rolling a dice and getting a divisor of 6 or 8 Divisors of 6: 1, 2, 3, 6 Divisors of 8: 1, 2, 4 We cannot count the 1 and 2 twice.

  6. Compound ProbabilityMutually inclusive The P(king or diamond) (there is a king of diamonds that can only be counted once) This is called mutually inclusive.

  7. Mutually Exclusive or Inclusive • A card is drawn from a standard deck of playing cards. Determine whether the events are mutually exclusive or not mutually exclusive. Then find the probability. • A. P(two or queen) • B. P(diamond or heart) • C. P(seven or club) • D. P(spade or ace)

  8. Compound Events • We can find the probability of two or more events happening. These are called compound events. • There are two types • Independent Events • Dependent Events

  9. Compound Events • When the outcome of one event doesnotaffect the outcome of a second event, theseare calledindependentevents. • The probability of two independent events isfound bymultiplyingthe probability of the first event by the probability of the second event.

  10. Independent Events Whatever happens in one event has absolutely nothing to do with what will happen next because: • The two events are unrelated OR • You repeat an event with an item whose numbers will not change (eg.: spinners or dice) OR • You repeat the same activity, but you REPLACE the item that was removed. The probability of two independent events, A and B, is equal to the probability of event A times the probability of event B.

  11. Independent Events P S O T R 6 1 5 2 3 4 Example: Suppose you spin each of these two spinners. What is the probability of spinning an even number and a vowel? P(even) = (3 evens out of 6 outcomes) (1 vowel out of 5 outcomes) P(vowel) = P(even, vowel) =

  12. Independent Events P S O T R 6 1 5 2 3 4 Example: Suppose you spin each of these two spinners. What is the probability of spinning an even number and a vowel? P(4, R) =

  13. Independent Events P S O T R 6 1 5 2 3 4 Example: Suppose you spin each of these two spinners. What is the probability of spinning an even number and a vowel? P(prime, consanant) =

  14. Independent Events Find the probability • P(jack, factor of 12) x =

  15. Independent Events Find the probability • P(face card, odd)

  16. Independent Events Find the probability • P(6, not 5) x =

  17. Independent Events Find the probability • P(2, not odd)

  18. Independent Events Find the probability • P(divisor of 6, not 5)

  19. Probability of independent Events A bag contains 6 black marbles, 9 blue marbles, 4 yellow marbles, and 1 green marbles. A marble is selected, replaced, and a second marble is selected. Find the probability of selecting; A black marble, then a yellow marble A blue marble, then a green marble Not a black marble, then a blue marble

  20. BASEBALL– Using experimental data • During the 1997 baseball season, the Florida Marlins won 5 out of 7 home games and 3 out of 7 away games against the San Francisco Giants. During the 1997 National League Division Series with the Giants, the Marlins played the first two games at home and the third game away. The Marlins won all three games. • Estimate the probability of this happening.

  21. Basketball • Chris keeps track of all his free throw and three point practice shots at home. He typically makes 3/8 of his free throws and 1/4 of his three point shots. • Today he took two free throws and two three point shots and made all of them. Based on his experimental data, what is the probability of this happening?

  22. Closure with a partner • 1) P(4, red) • 2) P(even, orange or green) • 3) P(prime, yellow, tails)

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