Question

A drawer contains 10 pairs of socks. Each pair is either black or white. What is the minimum number of socks that must be drawn, at random, from the drawer to ensure that you have 3 pairs of all the same color socks?

Answer #1

The solution to this problem is given by

Your sock drawer contains ten pairs of white socks and ten pairs
of black socks. If you're only allowed to take one sock from the
drawer at a time and you can't see what color sock you're taking
until you've taken it, how many socks do you have to take before
you're guaranteed to have at least one matching pair?

Your sock drawer contains 10 pairs of white socks and 4 pairs of
black socks. You reach in and pull out two pairs of socks in a row,
without replacement. Show Work.
What is the probability that the second pair is white, given
that the first pair is black?
What is the probability that the second pair is white, given
that the first pair is white?
What is the probability that the second pair is black, given
that the first...

A drawer contains four pairs of socks, with each pair a
different color. One sock at a time is randomly drawn from the
drawer until a matching pair is obtained.
Calculate the probability that the maximum number of draws is
required.
0.0006
0.0095
0.0417
0.1429
0.2286

Suppose your top drawer contains different colored socks: 8 are
white, 14 are black, 4 are pink, and 16 are blue. All socks in the
drawer are loose (unpaired). In the morning, you randomly select
two socks, one at a time. Calculate the following probabilities,
writing your answer either as a decimal or a fraction.
(a) What is the probability that you get a blue pair of
socks?
(b) What is the probability that you do not get a blue...

The drawer contains 10 white socks, 20 brown socks, 15 blue
socks, and 10 blacksocks. How many socks should be taken from the
drawer in complete darkness to besure that there is a matched
pair.

There are many socks with three diﬀerent colors in a drawer.
What is the minimum number of socks you have to choose to guarantee
there are two pairs of socks with the same color.

A drawer contains eight socks (eight total, not eight
pairs[which would be 16 socks total]), 2 are white, 1 is black, 3
are red, 1 is blue, and the last one is yellow.
1. What is the probability of choosing
a white sock, a black sock and a red sock in three draws?
2. What is the probability of choosing
a red sock first, and a black and a white sock, does not matter the
order for the last two?...

In
a sock drawer, you have a pair of blue socks, red socks, yellow
socks, orange socks, purple socks and green socks. You randomly
pull out a sock one at a time until you select a pair of matching
socks.
Let pr be the probability that you get your first matching
pair on the r’th sock pulled from the drawer.
Find pr for r = 2, 3, . . ..

Justin has 10 loose socks in a drawer, forming 5 pairs. But Justin
is careless and chooses two socks at random. What is the
probability that they will match?

(This is not pigeonhole) My drawer has n pairs of socks, fresh
from the laundry but all separated. Each sock is labeled “Left” or
“Right”. If I grab socks blindly, how many trials to I need to
guarantee a good pair? Please provide a step-by-step
explanation.

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