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Downunder87
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Probability, one doubt 24 Feb 2014, 04:44
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let's suppose we have 3 black balls and 2 red balls in a box. if we take out 4 balls WITH REPLACEMENT, which is the probability to get one red ball?
my strategy would be to suppose that the first ball is red so 2/5 and then consider 3 black balls. (3/5*3/5*3/5). then multiply all 2/5* (3/5^3) -->8.6%

I know it is wrong, but why??



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Bunuel
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Probability, one doubt 24 Feb 2014, 06:39
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Downunder87
let's suppose we have 3 black balls and 2 red balls in a box. if we take out 4 balls WITH REPLACEMENT, which is the probability to get one red ball?
my strategy would be to suppose that the first ball is red so 2/5 and then consider 3 black balls. (3/5*3/5*3/5). then multiply all 2/5* (3/5^3) -->8.6%

I know it is wrong, but why??
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Because the question asks about the probability of one ball being red, not the first ball being red. You can have the following 4 cases:
RBBB
BRBB
BBRB
BBBR

The probability of each case is 2/5*(3/5)^3, thus the overall probability is 2/5*(3/5)^3*4.

Theory on probability problems: math-probability-87244.html

All DS probability problems to practice: search.php?search_id=tag&tag_id=33
All PS probability problems to practice: search.php?search_id=tag&tag_id=54

Tough probability questions: hardest-area-questions-probability-and-combinations-101361.html

Hope it helps.
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gayam
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Probability, one doubt 26 Feb 2014, 16:21
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Downunder87
let's suppose we have 3 black balls and 2 red balls in a box. if we take out 4 balls WITH REPLACEMENT, which is the probability to get one red ball?
my strategy would be to suppose that the first ball is red so 2/5 and then consider 3 black balls. (3/5*3/5*3/5). then multiply all 2/5* (3/5^3) -->8.6%

I know it is wrong, but why??
Show more


You have done it 80% correctly, but here is the mistake...

if you remember the basics of the probability of permutations or combinations,
OR = +
AND = *

Here the red ball can be chosen 1st time or 2nd time or 3rd time or 4th time
that is the reason you will have to add 2/5 * (3/5)^3 4 times....
which is nothing but 4*2/5*(3/5)^3...

Hope this clarifies...



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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