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A student chooses a red marble from a Bag and Then chooses another red marble without replacing the first. is it independent or dependent ?

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1 Answer

Let say you have 10 marbles in the bag. 5 are blue and 5 are red.
 
First draw: if you want a red marble, you have 5 out of 10 chances to get it.
 
Second draw: since you dont put the first red marble back, it is not accounted for. So when you reach in the bag, you only have 4 out 9 chances of getting another red marble. 
 
So we can see clearly that the outcome of the 1st draw affects the out come of the 2nd draw; and hence it is dependent

Comments

No it is not:
  
  Let's take your assumption that there are 10 marbles of red and Blue 5 of each
 
  A - first draw be red
  B - 2nd draw be red ,then:
 
   Probability of 2nd draw to be red:
      
    A . B + A. B
    1/2 . 5/9 + 1/2 .4/9 = 5/18 + 4/ 18 = 9/18 = 1/2
 
     So the Probability of drawing Red marble without replacements is first draw or 2nd draw is the same 1/2.
     therefore the events are independent.
    probabilty Drawing 
 
 

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