Bunuel wrote:

arps wrote:

A box contains three pairs of blue gloves and two pairs of green gloves. Each pair consists of a left-hand glove and a right-hand glove. Each of the gloves is separate from its mate and thoroughly mixed together with the others in the box. If three gloves are randomly selected from the box, what is the probability that a matched set (i.e., a left- and right-hand glove of the same color) will be among the three gloves selected?

(A) 3/10

(B) 23/60

(C) 7/12

(D) 41/60

(E) 5/6

Let's calculate the opposite probability of NOT getting a matched set and subtract this value from 1.

This could happen only if we pick all three same hand BLUE gloves; two same hand BLUE gloves and any green glove;

or two same hand GREEN gloves and any BLUE glove

BBB: \(\frac{6}{10}*\frac{2}{9}*\frac{1}{8}=\frac{1}{60}\) (after we pick a blue glove, 6/10, then there is 2 same hand gloves left out of total 9 gloves - 2/9, and so on);

BBG: \((\frac{6}{10}*\frac{2}{9}*\frac{4}{8})*3=\frac{12}{60}\), multiplying by 3 as this scenario can occur in 3 different ways: BBG, BGB, GBB;

GGB: \((\frac{4}{10}*\frac{1}{9}*\frac{6}{8})*3=\frac{6}{60}\);

\(P=1-(\frac{1}{60}+\frac{12}{60}+\frac{6}{60})=\frac{41}{60}\).

Answer: D.

hope it's clear.

Dear

Bunuel, questions of this type actually give me hell.

I face problems in identifying what is unique or identical and what's not!

Here I at first thought that the socks of the same color and foot were identical, but I don't know if that's true. Then I thought that every pair is unique, which I also don't know. Please help me on how to comprehend questions of this type. How to actually translate and understand what's unique and what's not?

VeritasPrepKarishma your inputs are also most welcome.

_________________

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