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# M28-27

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Joined: 16 Jun 2018
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08 Oct 2018, 21:51
psych77 wrote:
Bunuel wrote:
Official Solution:

Certain bowl contains 5 red marbles and 3 blue marbles only. One by one, every marble is drawn at random and without replacement. What is the probability that the seventh marble drawn is NOT blue?

A. $$\frac{7}{8}$$
B. $$\frac{3}{4}$$
C. $$\frac{2}{3}$$
D. $$\frac{5}{8}$$
E. $$\frac{3}{8}$$

Basically we need to find the probability that the seventh marble drawn is red (so not blue).

Now, the initial probability of drawing red marble is $$\frac{5}{8}$$. Without knowing the other results, the probability of drawing red marble will not change for ANY successive draw: second, third, fourth, ..., seventh. Thus the probability that the seventh marble is red is $$\frac{5}{8}$$.

The same for blue marble: the probability of drawing blue marble is $$\frac{3}{8}$$, the probability that for instance the 8th marble drawn is blue is still $$\frac{3}{8}$$. There is simply no reason to believe WHY is any draw different from another (provided we don't know the other results).

Bunuel From what part of the question stem are we judging that we are unaware of the previous outcomes of other draws? How do we differentiate this question from other replacement questions where each number of marbles would be reduced with each draw.

chetan2u

can you help with this?
Re: M28-27   [#permalink] 08 Oct 2018, 21:51

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# M28-27

Moderators: chetan2u, Bunuel