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In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure how many draws did it take before the person picked a heart and won. What is the probability that there will be at least three draws involved in a win, i.e. someone picking her first heart on the third draw or later?

 Mar 3, 2020
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Probability  =

 

1  - P( heart  picked on first draw )    - P( heart picked on second draw  but not the  first)  

 

1  - 13/52   - ( 39/52)( 13/51)     =   

 

1 - 1/4 - (3/4)(13/51)    =

 

19/34  ≈  55.9 %

 

 

cool cool cool

 Mar 3, 2020

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