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1. What the the probability that both are Hearts?

Experiment: Draw 2 Cards Successively and Without Replacement From a Well-shuffled Deck of 52 Cards. H (12/51). 12 39 _ H H. 13 38 _ H H. 13 39 _ H H. H (13/52). Second card. _ H (39/51). First card. _ H (39/52). Second card.

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1. What the the probability that both are Hearts?

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  1. Experiment:Draw 2 Cards Successively and Without Replacement From a Well-shuffled Deck of 52 Cards

  2. H (12/51) 12 39 _ H H 13 38 _ H H 13 39 _ H H H (13/52) Second card _ H (39/51) First card _ H (39/52) Second card 1. What the the probability that both are Hearts?

  3. 13 38 _ H H H (13/51) _ H (38/51) 1. What the the probability that both are Hearts? P(1st H and 2nd H) = (13/52)(12/51) 12 39 _ H H H (12/51) 13 39 _ H H H (13/52) Second card _ P(1st H and 2nd H) = (13/52)(39/51) _ H (39/51) First card _ P(1st H and 2nd H) = (39/52)(13/51) _ H (39/52) Second card _ _ P(1st H and 2nd H) = (39/52)(38/51)

  4. 2. If the first card is a Heart, what the the probability that the second card is a Queen? 3 Q _ _ 12 Q 36 Q ______ Hearts Hearts 1 Q 3 Q _ _ 12 Q 36 Q ______ Hearts Hearts Q (3/51) Q (4/51) Q of H (1/52) Second card _ Q (48/51) _ Q (47/51) First card 1 Q 3 Q _ _ 11 Q 36 Q ______ Hearts Hearts OR _ Q and H (12/52) Second card

  5. 2. If the first card is a Heart, what the the probability that the second card is a Queen? 3 Q _ _ 12 Q 36 Q ______ Hearts Hearts 1 Q 3 Q _ _ 12 Q 36 Q ______ Hearts Hearts Q (4/51) Second card _ Q (47/51) First card 1 Q 3 Q _ _ 11 Q 36 Q ______ Hearts Hearts Second card P(1st Q of H and 2nd Q) = (1/52)(3/51) Q (3/51) Q of H (1/52) _ Q (48/51) OR _ Q and H (12/52)

  6. 2. If the first card is a Heart, what the the probability that the second card is a Queen? 3 Q _ _ 12 Q 36 Q ______ Hearts Hearts 1 Q 3 Q _ _ 12 Q 36 Q ______ Hearts Hearts Second card First card 1 Q 3 Q _ _ 11 Q 36 Q ______ Hearts Hearts Second card P(1st H and 2nd Q) = (1/52)(3/51) + (12/52)(4/51) P(1st Q of H and 2nd Q) = (1/52)(3/51) Q (3/51) Q of H (1/52) OR (+) _ Q (48/51) _ P(1st (Q and H) and 2nd Q) = (12/52)(4/51) OR Q (4/51) _ Q and H (12/52) _ Q (47/51)

  7. 2. If the first card is a Heart, what the the probability that the second card is a Queen? P(1st H and 2nd Q) = (1/52)(3/51) + (12/52)(4/51) But we want to find P(2nd is Q | 1st is H) which is: P(2nd Q and 1st H) = (1/52)(3/51) + (12/52)(4/51) = (1/13) P(1st H) (13/52)

  8. Q (3/51) 3 48 _ Q Q 4 47 _ Q Q 4 48 _ Q Q Q (4/52) Second card _ Q (48/51) First card Q (4/51) _ Q (48/52) Second card _ Q (47/51) 3. What the the probability that the second card is a Queen?

  9. 3 48 _ Q Q 4 47 _ Q Q 4 48 _ Q Q Second card First card Q (4/51) Second card _ Q (47/51) 3. What the the probability that the second card is a Queen? P(1st Q and 2nd Q) = (4/52)(3/51) Q (3/51) Q (4/52) _ Q (48/51) OR _ Q (48/52)

  10. 3 48 _ Q Q 4 47 _ Q Q 4 48 _ Q Q Second card First card Second card Answer = (4/52)(3/51) + (48/52)(4/51) = (1/13) 3. What the the probability that the second card is a Queen? P(1st Q and 2nd Q) = (4/52)(3/51) Q (3/51) Q (4/52) OR(+) _ Q (48/51) OR _ P(1st Q and 2nd Q) = (48/52)(4/51) Q (4/51) _ Q (48/52) _ Q (47/51)

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