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Compound probability

Compound probability. M408 Probability Unit. When ‘A’ and ‘b’ are independent. Example 1 – Pick a card from a deck. Replace the card in the deck, then pick again. What is the probability you pick a heart on the 1 st pick and a heart on the 2 nd pick?.

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Compound probability

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  1. Compound probability M408 Probability Unit

  2. When ‘A’ and ‘b’ are independent • Example 1 – Pick a card from a deck. Replace the card in the deck, then pick again. What is the probability you pick a heart on the 1st pick and a heart on the 2nd pick?

  3. Dependent events: they do affect each other. • The occurrence of “8 inches of snow” affects the probability of “school cancelled.” • “Not studying” affects the chance of “getting an A on the test.” • If A and B are dependent, then the chance of ‘A’ happening my increase or decrease depending on whether or not ‘B’ happens.

  4. Dependent events: they do affect each other. • Example 2 – Pick one card from the deck, and then pick a second card without replacing the first one. P(Heart on 1st pick and Heart on 2nd pick) =

  5. Ex 3 – 5 red, 3 yellow, 4 green, and 3 orange peppers are mixed up in a rucksack from the farmer’s market. A.) Find the probability of picking a red, followed by a green, followed by another green, all without replacement. B.) Find the probability of randomly picking three peppers, and getting a red and two greens. C.) What is the difference between (A) and (B)?

  6. Ex 4 – pick one card from a standard deck. Are the following events dependent or independent? A.) P(card is a King AND it is black) Does knowing that a card is a King change the prob. it could be black? B.) P(card is a Club AND it is black) Does knowing that a card is a Club change the prob. it could be black?

  7. Ex 4 – pick one card from a standard deck. Are the following events dependent or independent? C.) P(card is red AND it is black) Does knowing that a card is red affect the prob. that it could be black? This is an example of Mutually Exclusive Events.

  8. Mutually exclusive events: can’t occur at the same time. Also known as ‘disjoint’ events. Examples: Roll an even number AND an odd number on one die. Flip heads and tails at the same time on one coin. Mutually Exclusive Events are Dependent, because if one of the events happens, the prob. of the other event happening becomes 0.

  9. Why subtract P(A and B)? Think about rolling a die… what is P(multiple of 2 OR multiple of 3)?

  10. Ex 5 – Standard deck of cards. Pick one. A.) P(King OR a black card) B.) P(King OR a Queen) C.) Which pair of events are mutually exclusive? D.) Which pair of events are independent?

  11. Ex 6 – roll a red die and a green die. (consult your table) A.) P(sum is 8 or sum is odd) B.) P(sum is 8 or doubles are rolled) C.) Which pair of events are mutually exclusive? D.) Which pair of events are independent?

  12. Ex 7 – pick a card and roll a die at the same time. A.) P(pick a King OR roll an odd number) B.) Which of the following phrases describe the events above? Independent, Dependent, Mutually Exclusive

  13. Ex 8 – pick two cards from a standard deck. A.) P(both are Aces OR both are Black)

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