Deceptive little question bugger

At the first look, one might feel that the knowledge of the ratio of the number of

Green to

Blue chips is sufficient to calculate the probability that is being asked. Let's go down this rabbit hole for a second...

Blue Chips :

Green Chips =

3 :

4 Lets convert the ratios into

absolutes.Let # of Blue Chips =

3xLet # of Green Chips =

4xTotal # of Chips =

7xProbability of picking up 2 Blue chips in successive attempts = P (Blue in first attempt) * P(Blue in second attempt ).

[*]Probability (Blue in first attempt) = 3x/7x

[*]After the first attempt, the total # of blue chips = 3x - 1

[*]After the first attempt, the total # of chips = 7x - 1

Probability of picking up

blue chip in the

second attempt :

( 3x-1)/(7x-1) Required probability of picking up two successive blue chips = (3x/7x) * (3x-1)/(7x-1)

No matter what we do, we cannot eliminate the "x".

Hence (A) is not sufficient

The key take away from this question is that,

given the ratio of the number of Green : Blue chips, , we can always find out the probability of picking either colored chip in the

first attempt.

However, the probability of picking up the second chip - be it blue or green - cannot be determined

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