Two marbles are drawn in succession from a box containing 10 red, 30

Question

Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue, and 15 orange marbles, replacement being made after each drawing. What is the probability that both are white?

(A) 11/15 
(B) 16/25 
(C) 64/225 
(D) 4/25 
(E) 4/75

chetan2u · Answer

Total marbles : 10+30+20+15=75

1) Both white  
P of W-W =  \frac{30}{75}*\frac{30}{75}=\frac{4}{25}

D

Bunuel · Answer

Saammm · Answer

Could you please clarify my doubt and let me know where I might be going wrong?

Since it’s stated that two marbles are being drawn consecutively, shouldn’t the probability be calculated as:

(30/75) * (29/74) ?

Initially, there are 30 white marbles. After drawing one, 29 remain, leading to this conclusion.

I’m basing this approach on similar probability questions of the similar type.

Bunuel · Answer

You are missing the highlighted part in the stem:  ...replacement being made after each drawing.  This means that when a marble is drawn, it is put back, so the second draw is again from 75 total marbles, not 74. Similarly, if a white ball is drawn, it is put back, so for the second draw, we still have the initial number of white balls: 30.

Hope it's clear.

Two marbles are drawn in succession from a box containing 10 red, 30

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Two marbles are drawn in succession from a box containing 10 red, 30

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