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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 ?

Is this independent or dependent ?

### 1 Answer by Expert Tutors

TrungThanh B. | Math and Science TutorMath and Science Tutor
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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

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