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Socks in a Drawer A drawer contains 11 identical red socks and 8 identical black socks. Suppose that you choose 2 socks at random in the dark.$$\begin{array}{l}{\text { a. What is the probability that you get a pair of red }} \\ {\text { socks? }} \\ {\text { b. What is the probability that you get a pair of black }} \\ {\text { socks? }} \\ {\text { c. What is the probability that you get 2 unmatched }} \\ {\text { socks? }} \\ {\text { d. Where did the other red sock go? }}\end{array}$$

a. 0.322 b. 0.164 c. 0.515d. It probably got lost in the wash!

Intro Stats / AP Statistics

Chapter 4

Probability and Counting Rules

Section 5

Sampling and Data

Probability Topics

University of North Carolina at Chapel Hill

Cairn University

Oregon State University

Lectures

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PROBLEM SOLVING A drawer c…

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Determine whether the even…

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03:16

Okay, So in this question, they're asking us what is the probability that out off 11 salt servant on in this 11 thoughts, you're getting a pair off Red Sox. So we know there are 11 Red Sox server on eight, black subservient. Okay. And you're selecting to source today. So total number of ways we can select to stocks will be cool toe. Totally. Consider 19 pair of salt circle. So 19, you're selecting two songs since 1932 will be the total number of us and you see two. We've confined 19 to 18 by two. That is a call to you. Can one 71 No welcoming the first part off the question. What is the problem with that? You get a pair off Red Sox. The probability of getting pair off Red Sox so you can see there are 11 Red Sox Are there out of that year selected to That will be done favorable case and we already found out Total number of case will be 1960 11, 32. It will be good for different 19 state to be already found on 1 71 55.717 day one will be the required probability that we can produce in 2.3216 That'll be the answer for first part of the question. Now, in the second part, that is asking, What is the problem to that? You get a pair off black sauce, pair off black spots, the pair of black socks you consider a two black socks server out off that your selective, too, on total number of ways we can select to talk serious. 1982 Now 82. Well, we confined. We get it is 28 by 1 71. Welcome. Now we can reduce this in 2.1637 This'll be required, probably for second part of the question. The third pot. He's asking, What is the property that you get to unmatched results? I matched the socks that ask him. It's one south care. Selecting will be correct. One will be black. So one red on one black, that is. What is the meaning off on matter socks, Right, So one Red Sox meals you're selecting out off level that you can do by 11 C one ways. Similarly, one black socks can select by using 87 ways divided by your daughter. Number of ways will be 19 sick. Okay, so 11 7 makes it will be 11 87 You find out 8 19 seats. We already found it is 1 71. So we get 88 by 1. 71. This is equal to 0.5146 This will be required. A probability? Mhm. Okay, then. Now there's a last hostilities asking What? What happened to them? They are off Red Sox. That is nothing has to do with the probability. So even Right. Answer. Like probably removing lost in wash. Okay. Okay, so this is D required answer for supporting costume.

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