Question

A deck of cards is divided randomly into two stacks A and B of 14 and...

A deck of cards is divided randomly into two stacks A and B of 14 and 38 cards respectively. You pick a card from the decks, what is the probability of drawing:

(a) An ace of hearts from stack A?

(b) An ace of hearts from stack B?

(c) Are the above two events independent?
Math   Statistics-And-Probability   
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Homework Answers

Answer #1

a) Let S be the event that an ace of heart is drawn and T be the event that the ace of heart is in stack A . Note that there is only one ace of heart in the deck .  

So,

to find  

We know

b) Similarly let U be the event that ace of heart is in stack B

So ,

  

c) Note that there is only one ace of heart in the deck . It can either go to stack A or to stack B . So, the occurrence of one event indicates non occurrence  of the other . So they cannot be independent .

Mathematically : If A be the event in (a) and B be the event in (b)

P[A B] =  0 . But none of the event has probability 0 individually . So they are not independent .

  

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