"Draw one card from a standard deck of playing cards. Let’s examine the independence of 3 events ‘the card is an ace’, ‘the card is a heart’ and ‘the card is red’. Define the events as A = ′ a c e ′ , H = ‘ h e a r t s ′ , R = ‘ r e d ′ ."With P ( A ) = 1 13 , P ( H ) = 1 4 and P ( R ) = 1 21 I get 1 4 for P ( H | R ). So this basically says that P(H) and P(R) are independent, since H and P are independent iff P ( H | R ) = P ( H ) . I know that that's not correct from the source, so now I am wondering how I can then calculate the conditional probability for dependent events and how I would know beforehand. Why is P ( H | R ) actually 1 2 ?

Question

&quot;Draw one card from a standard deck of playing cards. Let’s examine the independence of 3 events ‘the card is an ace’, ‘the card is a heart’ and ‘the card is red’. Define the events as   A      =    ′    a  c      e    ′  ,   H  =  ‘  h  e  a  r  t      s    ′  ,   R  =  ‘  r  e      d    ′  .&quot;With   P  (  A  )  =      1    13    ,     P  (  H  )  =      1    4   and   P  (  R  )  =      1    21   I get       1    4   for   P  (  H      |    R  ). So this basically says that P(H) and P(R) are independent, since H and P are independent iff   P  (  H      |    R  )  =  P  (  H  ) . I know that that&#039;s not correct from the source, so now I am wondering how I can then calculate the conditional probability for dependent events and how I would know beforehand. Why is   P  (  H      |    R  ) actually       1    2   ?

Cristian Delacruz · Accepted Answer

Step 1  P  (  H      |    R  ) means you already know the card is red, so your total pool is 26 red cards. from these 26 red cards, you want to know the probability for selecting a heart, so there are 13 heart cards, therefore, you have  P  (  H      |    R  )  =      12    26    =      1    2

"Draw one card from a standard deck of playing cards. Let’s examine the independence of 3 events ‘the card is an ace’, ‘the card is a heart’ and ‘the card is red’. Define the events as A = ‘ace’, H = ‘hearts’, R = ‘red’."

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