Answers.Body: <p><strong>55 Bags</strong></p>
  
  <p>If the distribution is assumed to be completely random (not necessarily true), and of a large enough group to make your purchases not effect the total probability (likely) then this is an alternate of a classic math problem known as the Coupon Collector's Problem:</p>
  
  <p><a href="https://en.wikipedia.org/wiki/Coupon_collector%27s_problem" rel="noreferrer">https://en.wikipedia.org/wiki/Coupon_collector%27s_problem</a></p>
  
  <p>There are many discussions of this and other probability problems in the Mathematics Stack Exchange.</p>
  
  <p>Avoiding all the maths The answer for 16 individual units is 55.</p>
  
  <p>If they have a case of 60 with a guaranteed full set, personally I'd buy it rather than depend on the random distribution of bags.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-06-29T20:46:53.067Z
Answers.Text: This is a great explanation of the maths. Note, however, that the distribution of figures is not completely random: there are more of some figures than others.
Answers.UserDisplayName: Kramii
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Answers.CreationDate: 2016-06-29T20:59:11.287Z
Answers.Text: I agree it wouldn't be random, but it was an assumption listed in the question itself. Without knowing the actual distribution there is no way to solve the problem without making some assumptions.
Answers.UserDisplayName: Josh King
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Answers.CreationDate: 2016-06-29T14:28:52.020Z
Answers.LastActivityDate: 2016-06-29T14:28:52.020Z
Answers.UserDisplayName: Josh King
Answers.Body: <p><strong>16 Bags</strong></p>
  
  <p>I know the question was phrased as a sort of math problem, but most LEGO fans solve it as a sort of LEGO problem. The bags are opaque, so you cannot see what's in the bags, but almost everywhere they are sold you can feel the bags, and you can determine what figure is in the bag. With the exception of the recent Soccer Team figures, collectible minifigures are always unique in terms of what parts are in the bag. Just shake and squeeze the bag until the distinctive piece is found.</p>
  
  <p>The problem with the math way: One can compute the probability of, say, picking two matching socks out of a drawer of miscellaneous socks, or of picking a whole collection of figures out of a box of figures. But there are a few complications:</p>
  
  <ul>
  <li>Someone else has been there before you and squeezed the bags to find all the space marines.</li>
  <li>Someone else has been there before you and grabbed a few at random, but then squeezed a few more bags to find the Princess.</li>
  <li>The store takes what's left from the first box and jams it into the second box when the box runs low; or they don't even display them in the original box, making it impossible to know how many boxes are in play and how many figures have been picked.</li>
  <li>There are usually 16 figures in a collection and 60 figures in a box; this means the figures cannot be evenly distributed. Some series have had as few as two of one figure in the box. Given that, it's entirely possible (though unlikely) to pick 58 figures and miss both of that elusive Unicorn Girl.</li>
  </ul>
  
  <p>If squeezing the bags isn't an option, the only way to be sure is to buy a new, unopened box.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-06-29T20:00:40.387Z
Answers.LastActivityDate: 2016-08-11T19:34:08.007Z
Answers.LastEditDate: 2016-08-11T19:34:08.007Z
Answers.UserDisplayName: Mr. Shiny and New 安宇
Body: <p>There are <a href="http://images.brickset.com/sets/images/71011-17.jpg" rel="nofollow noreferrer">16 distinct LEGO minifigures</a> in a collectible series. They are sold individually in <a href="http://images.brickset.com/sets/images/71011-0.jpg" rel="nofollow noreferrer">"mystery" bags</a> so that you cannot tell which one is inside. </p>
  
  <p><a href="https://i.sstatic.net/5sZFI.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/5sZFI.jpg" alt="Minifigures"></a></p>
  
  <p><strong>To get all 16 minifigures, what's the expected number of bag purchases I need to make?</strong> </p>
  
  <p>For simplicity let's make the assumption that the probability of a single bag containing a specific minifigure always is 1/16. </p>
  
  <p>In fact, you may sometimes be able to buy <a href="http://legogenre.com/wp-content/uploads/2015/12/Lego_Minifigures_Series15_71011_Box.jpg" rel="nofollow noreferrer">a case</a> with 60 of these bags, <a href="https://bricks.stackexchange.com/questions/6449/is-there-a-standard-distribution-of-minifigs-when-you-purchase-an-entire-case">guaranteed to contain the complete series</a>. And you may <a href="http://swap.minifiguresseries.com/#" rel="nofollow noreferrer">swap figures on the Internet</a>. Let's ignore such options for this question.</p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2016-06-29T08:55:49.780Z
Comments.Text: Well you might need to add in how many you pick from a certain box, or is it a mix of 10 boxes, this all would increase the probabilities etc. I think using a bred new open box (which should contain min 2 full sets) you should be able to work out the math there I just feel the bags and 98% of the time get the one I want and if I have the time ill feel for a whole series in one hit from a Lego store and get a good 90% of the series (like the recent disney ones)
Comments.UserDisplayName: Adam Mann Pro
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2016-06-29T09:02:29.080Z
Comments.Text: @Adam Mann Pro: Where I purchase these bags there are hundreds of them mixed in big boxes. And I don't have the talent to "feel" the contents with my fingers, hence the assumption that what I get is truly random.
Comments.UserDisplayName: Gruber
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2016-06-29T09:05:27.547Z
Comments.Text: your odds seem quite high then, as they might be the duplicates from many boxes. if you were looking to sell them people are still willing to buy them opened (with all bags, accessories etc) as they will be guaranteed to get the one they want.
Comments.UserDisplayName: Adam Mann Pro
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2016-06-29T11:49:31.470Z
Comments.Text: There are lots of folks on ebay who will sell you a complete unopened set.  I bought one and it was complete and the bags were still perfectly sealed.
Comments.UserDisplayName: chicks
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2016-06-29T20:53:25.587Z
Comments.Text: Even if you can feel out a couple of figures, that can increase your odds of getting a complete set quite considerably. For example, the wedge-shaped "skirt" of many female figures is often easy to identify. The short, non-jointed legs are only a little harder, as are accessories like 2x2 tiles. I recommend giving it another go: you might surprise yourself.
Comments.UserDisplayName: Kramii
Tags: <collectable-minifigures>
Title: How many mystery collectiable minifig bags to buy to get them all?
UserDisplayName: Gruber
ThreadText: # How many mystery collectiable minifig bags to buy to get them all?
  
  (Asked by: username_0 on 2016-06-29)
  
  There are [16 distinct LEGO minifigures](http://images.brickset.com/sets/images/71011-17.jpg) in a collectible series. They are sold individually in ["mystery" bags](http://images.brickset.com/sets/images/71011-0.jpg) so that you cannot tell which one is inside.
  
  [![Minifigures](https://i.sstatic.net/5sZFI.jpg)](https://i.sstatic.net/5sZFI.jpg)
  
  **To get all 16 minifigures, what's the expected number of bag purchases I need to make?**
  
  For simplicity let's make the assumption that the probability of a single bag containing a specific minifigure always is 1/16.
  
  In fact, you may sometimes be able to buy [a case](http://legogenre.com/wp-content/uploads/2015/12/Lego_Minifigures_Series15_71011_Box.jpg) with 60 of these bags, [guaranteed to contain the complete series](https://bricks.stackexchange.com/questions/6449/is-there-a-standard-distribution-of-minifigs-when-you-purchase-an-entire-case). And you may [swap figures on the Internet](http://swap.minifiguresseries.com/#). Let's ignore such options for this question.
  
  **Tags:** collectable-minifigures
  > **Comments:**
  > **username_1**: Well you might need to add in how many you pick from a certain box, or is it a mix of 10 boxes, this all would increase the probabilities etc. I think using a bred new open box (which should contain min 2 full sets) you should be able to work out the math there I just feel the bags and 98% of the time get the one I want and if I have the time ill feel for a whole series in one hit from a Lego store and get a good 90% of the series (like the recent disney ones)  
  > **username_0**: @Adam Mann Pro: Where I purchase these bags there are hundreds of them mixed in big boxes. And I don't have the talent to "feel" the contents with my fingers, hence the assumption that what I get is truly random.  
  > **username_1**: your odds seem quite high then, as they might be the duplicates from many boxes. if you were looking to sell them people are still willing to buy them opened (with all bags, accessories etc) as they will be guaranteed to get the one they want.  
  > **username_2**: There are lots of folks on ebay who will sell you a complete unopened set.  I bought one and it was complete and the bags were still perfectly sealed.  
  > **username_3**: Even if you can feel out a couple of figures, that can increase your odds of getting a complete set quite considerably. For example, the wedge-shaped "skirt" of many female figures is often easy to identify. The short, non-jointed legs are only a little harder, as are accessories like 2x2 tiles. I recommend giving it another go: you might surprise yourself.  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_4 on 2016-06-29. Score: 5 | Accepted answer
  
  **55 Bags**
  
  If the distribution is assumed to be completely random (not necessarily true), and of a large enough group to make your purchases not effect the total probability (likely) then this is an alternate of a classic math problem known as the Coupon Collector's Problem:
  
  <https://en.wikipedia.org/wiki/Coupon_collector%27s_problem>
  
  There are many discussions of this and other probability problems in the Mathematics Stack Exchange.
  
  Avoiding all the maths The answer for 16 individual units is 55.
  
  If they have a case of 60 with a guaranteed full set, personally I'd buy it rather than depend on the random distribution of bags.
  
  > **Comments:**
  > **username_3**: This is a great explanation of the maths. Note, however, that the distribution of figures is not completely random: there are more of some figures than others.  
  > **username_4**: I agree it wouldn't be random, but it was an assumption listed in the question itself. Without knowing the actual distribution there is no way to solve the problem without making some assumptions.  
  
  ---
  
  ### Answer by username_5 on 2016-06-29. Score: 6
  
  **16 Bags**
  
  I know the question was phrased as a sort of math problem, but most LEGO fans solve it as a sort of LEGO problem. The bags are opaque, so you cannot see what's in the bags, but almost everywhere they are sold you can feel the bags, and you can determine what figure is in the bag. With the exception of the recent Soccer Team figures, collectible minifigures are always unique in terms of what parts are in the bag. Just shake and squeeze the bag until the distinctive piece is found.
  
  The problem with the math way: One can compute the probability of, say, picking two matching socks out of a drawer of miscellaneous socks, or of picking a whole collection of figures out of a box of figures. But there are a few complications:
  
  * Someone else has been there before you and squeezed the bags to find all the space marines.
  * Someone else has been there before you and grabbed a few at random, but then squeezed a few more bags to find the Princess.
  * The store takes what's left from the first box and jams it into the second box when the box runs low; or they don't even display them in the original box, making it impossible to know how many boxes are in play and how many figures have been picked.
  * There are usually 16 figures in a collection and 60 figures in a box; this means the figures cannot be evenly distributed. Some series have had as few as two of one figure in the box. Given that, it's entirely possible (though unlikely) to pick 58 figures and miss both of that elusive Unicorn Girl.
  
  If squeezing the bags isn't an option, the only way to be sure is to buy a new, unopened box.
  
  
  ---
  
  