Tom is off to a school Annual Day and is searching for a matching pair of socks. The same result as before, and, similarly for the other colors. Answer To Amazon’s Pair Of Socks Puzzle The tempting answer is 50 percent. Join in and write your own page! There are $\displaystyle C^{r+b+g}_{2}$ ways to select $2$ socks out of the total of $r+b+g.$ There are $\displaystyle C^{r}_{2}$ ways to select $2$ out $r$ red socks. Start Now. Case 2 : 2 pair of socks are present in the drawer. This question was asked in Aamaon. P(2\mbox{ red socks})&=C^{r}_{2}/C^{r+b+g}_{2}\\ by Clarence Print the number of Draws (x) Tom makes in the worst case scenario. Hence, 3. Logging in registers your "vote" with Google. Problem: There are 6 pairs of black socks and 6 pairs of white socks.What is the probability to pick a pair of black or white socks when 2 socks are selected randomly in darkness.

The 3rd sock picked will definitely match one of previously picked socks.

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If you like this Page, please click that +1 button, too. Simply click here to return to. Socks of the same color are identical but not allowed to look into the drawer while taking out socks. Solution 1 To start with, instead of looking for a matching pair, let's find the probability that both socks are red. Signup and start solving problems. If you write up a matrix 6*6 with four reds and two blues on each dimension, you can easily count the probability. The formula is eminently reasonable, for if any of the three numbers is $1,$ the effect of having an unmatched sock in a drawer is to increase the denominator without adding anything to the numerator. Hence, 3. |Algebra| The students get confused.

The answer to this is, $\displaystyle\frac{4\cdot 3+5\cdot 4+2\cdot 1}{11\cdot 10} = \frac{17}{55}.$, |Contact| (If you are not logged into your Google account (ex., gMail, Docs), a login window opens when you click on +1. Sock Merchant: hackerrank problem easy solution in java,C++ Get link; Facebook; Twitter; Pinterest; Email; Other Apps ; February 17, 2017 John's clothing store has a pile of loose socks where each sock is labeled with an integer, , denoting its color. His drawer is filled with socks, each pair of a different color. He wants to sell as many socks as possible, but his customers will only buy them in matching pairs. Next T lines contains an integer N which indicates the total pairs of socks present in the drawer. We care about your data privacy. }\\ Thank you!). It's easy to do.

Case 1 : A pair of socks are present, hence exactly 2 draws for the socks to match. Do not try solving the whole problem at once but try to think of more manageable subproblems. HackerEarth uses the information that you provide to contact you about relevant content, products, and services. What is the probability of getting a matching pair? The first and the second draw might result in 2 socks of different color. Staff www.solving-math-problems.com |Front page| Explanation: Case 1: Same sock color come out in 1st and 2nd attempt- &=\frac{r(r-1)}{(r+b+g)(r+b+g-1)}.

The chance of getting a matching pair of socks is 7 out of 15 >>> the final answer to your question is: 7/15 Thanks for writing. It's easy to do. So the probability of selecting two red socks is, \begin{align}\displaystyle The first and the second draw might result in 2 socks of different color. The following solution uses the Principle of Inclusion / Exclusion, abbreviated PIE. Simply click here to return to Math Questions & Comments - 01. Answer: 3. If you like this Site about Solving Math Problems, please let Google know by clicking the +1 button. So, the task is to find the minimum number of socks to be drawn at random to be sure that he/she gets the pair of socks of the same color? The probability of getting one sock red is\displaystyle\frac{r}{r+b+g}.$Assuming that the first sock is red, the probability of getting the second red sock is$\displaystyle\frac{r-1}{r+b+g-1}.$, When it comes to calculating probabilities, colors do not make much difference: analogous argument applies to blue and green socks, implying that the probability of getting two blue socks is$\displaystyle\frac{b(b-1)}{(r+b+g)(r+b+g-1)}$and that of getting green socks is$\displaystyle\frac{g(g-1)}{(r+b+g)(r+b+g-1)}.$The answer to the question is then,$\displaystyle\frac{r(r-1)+b(b-1)+g(g-1)}{(r+b+g)(r+b+g-1)}.. If you simply break it down and separate it, they can get it. Comparing Two Fractions Without Using a Number Line, Comparing Two Different Units of Measurement, Comparing Numbers which have a Margin of Error, Comparing Numbers which have Rounding Errors, Comparing Numbers from Different Time Periods, Comparing Numbers computed with Different Methodologies, Exponents and Roots Properties of Inequality, Calculate Square Root Without Using a Calculator, Example 4 - Rationalize Denominator with Complex Numbers, Example 5 - Representing Ratio and Proportion, Example 5 - Permutations and combinations, Example 6 - Binomial Distribution - Test Error Rate, Join in and write your own page! Note: Not all browsers show the +1 button. The 3rd sock picked will definitely match one of previously picked socks. As you can see, there are 7 combinations of matching socks out of 15 possible combinations. This is too complicated. &=\frac{r!}{2!(r-2)!}\cdot\frac{2!(r+b+g-2)!}{(r+b+g)! \end{align}.

Case 1 : A pair of socks are present, hence exactly 2 draws for the socks to match. Case 2 : 2 pair of socks are present in the drawer. How?

To start with, instead of looking for a matching pair, let's find the probability that both socks are red.

The Sock Drawer: Probability and Statistics Problem A drawer contains red socks and black socks. Two drawn at random. When two socks are drawn at random, the probability that both are red is 1/2. That should be what you do first with an easy assignment as this. It would seem you can either make a pair or have a mismatched pair, and that both of those events would have equal chances, making for a 50 percent probability. (Deatsville, AL, USA). In a drawer $r$ red, $b$ blue, and $g$ green socks.

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