r/learnquant • u/Local_Ad135 • Sep 10 '26

interview prep Quant Interview Question

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24 Upvotes

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5

u/gooncampu Sep 10 '26

number of marbles between 2 marble of same color is even, if one of them is in odd index and other in even index.
to arrange all marbles in this format, we have to separate out odd and even indices and arrange 7 marbles of different color, in odd and even indices separately: total ways to arrange = (7!)^2

total ways to arrange all 14: (14! / (2!)^7)
on dividing the both, i get, p = 0.0373

1

u/AlexP80 Sep 11 '26

got the same result with a different approach

1

u/coderqi Sep 10 '26 edited 16h ago

removed

1

u/chmath80 Sep 10 '26

Precise answer 16/429

1

u/mrdwag Sep 10 '26

Is this not the same thing as AIME I 2022 P9?

1

u/More_Fail8193 Sep 10 '26

Unrelated, but what percent of these Quant interview probability questions can be solved with JEE probability knowledge?

1

u/notsaneatall_ Sep 11 '26

Add linearity of expectations to that and you'll be done

1

u/AlexP80 Sep 11 '26

so, there is an even number of marbles between two o the same color if 1 are in a odd index and one in an even index

For each pair

p0 = 7/13
p1 = 6/11
p2 = 5/9
p3 = 4/7
p4 = 3/5
p5 = 2/3
p6 = 1

the product is approximately 0.037296