Secret Santa: What Is The Probability That Someone Pulls Her Own Name From A Hat
Each year my siblings choose names for a Christmas gift exchange. It is not unusual for a sibling to pick her own name, whereupon the name is replaced into the hat and a new name is drawn. In fact, that “glitch” in the drawing process was a motivation for me to write a program that automates the Christmas gift exchange because my program ensure that no sibling gives to himself or to his spouse.
Last week I got an email from a reader whose wife had pulled her own name while participating in a Secret Santa gift exchange. There were 10 names in the hat, and the reader wanted to know the probability of someone pulling her own name. He wrote a SAS/IML simulation program that estimated the probability for various group sizes. His simulation indicated that for six or more people, there is only a 36.8% chance that no person pulls her own name. What was surprising is that for moderate-sized groups, the probability is independent of the size of the group!
The reader wondered whether I could explain this strange number and why the probability is independent of the group size.
How To Draw Anime Explorer Hat Step By Step
The explorer hat is often worn by anime characters that are on some sort of an adventure, often in a jungle type environment.
Stat by drawing an outline of the head and hair.
Draw the top part of the explorer hat as close to a half circle in shape and a much lighter curve for its bottom. Make the brim fairly short. Draw its shape following the bottom curve of the top part of the head a slight distance away and then sticking out a little bit more to the sides.
For the finishing touches you can add the split lines between the different panels that are so icon of these explorer hats along with a button like shape on the very top.
To show the panels simply draw a pair of curved lines from each side of the hat towards its top tip and add the button at the very top where those lines meet.
Finish the drawing by adding some basic hair details.
You can see a close up drawing of the explorer hat above along with some basic hair shading.
Start Drawing The Tassel Of The Hat
Graduation hats will generally have a tassel dangling from the top of the hat. In step 3 of this guide on how to drawa graduation hat, we will be starting with this aspect.
First, we will be drawing the string that the tassel will be attached to. To draw this string, draw a curved line from the button on top of the hat that trails off to the side so that it is hanging off the edge.
Then, draw another line running closely next to it to finish off the string.
With that string complete, we will then draw a circle at the end of the string, as this is what the tassel will attach to later.
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Draw The Other Side Of The Brim
Now it is time to draw the other side of the brim. Continue with the seam line from the front of the brim and extend this line running parallel to the brim outline and all the way to the base of the crown.
After that, make these two parallel lines longer so they overlap the hat band we drew earlier. If you recall from before, I said the brim will conceal the back of the hat band. This is our way of bringing this portion of the brim to the foreground and pushing the hat band and rest of the crown farther into the background. Be careful that you dont bring these two lines too far above the hat band like Im doing here. This is a mistake that I need to fix.
Slowly begin to curve the top line as soon as it goes beyond the top of the hat band. The tilt beyond this curve should be at the same angle as the brim on the other side. Then curve the bottom line before it reaches the top of the hat band, keeping the curve parallel to the first curved line.
How To Draw Anime Wizard Hat Step By Step
The wizard hat is very common to fantasy anime and usually tends to be worn by female characters.
Start by drawing an outline of the head/hair and draw the hat over top of this.
The entire hat should be somewhat similar in shape to an upside down ice cream cone but with the top part hanging to one side.
To show that the hat is tilted slightly upwards show some of its underside by drawing a pair of lines going from the bottom left and right tips of the hat towards the ears. These lines will define the inner/background part of the at.
Erase the parts of the head and hair that are covered by the hat after you are done drawing its outer shape.
To finish the drawing you can add a little band around the area where wizard hat transitions from the brim to the top. You can also draw the details of the hair.
You can see a larger finished drawing of the wizard hat above with some basic shading.
You may noticed that the background/inner portion of the hat is shaded slightly darker then the rest as usually less light will reach there.
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How To Draw Anime Winter Hat Step By Step
Somewhat similar to the previous example is the winter hat with the pom pom. This is another very common item for female anime characters to ware during winter.
Draw the head with the outline of the hair.
Add the top part of the hat as one big curve that is farther away form the head on top and closer to it on the sides. Next draw the bottom part of the hat wrapping around the hair/head. Finally add the pom pom as pretty much a circle that is partially hidden behind the the hat.
Once done erase the parts of the head and hair covered by the hat.
Around the circle of the pom pom draw the fluff in small pointy clumps of slightly different size similar to the example above. Erase the circle line once done.
To make the hat look a little more interesting you can add some lines along its bottom as a small design element. Draw the lines farther apart towards the middle of the head and closer together as they move to the sides. This will help show that the hat is actually wrapping around the head.
You can finish the drawing by adding the details of the hair.
Above you can see the finished drawing of the winter pom pom hat with some basic shading.
Permutations To The Rescue
I was intrigued. Mathematically, pulling names from a hat is equivalent to a permutations of the numbers 1n. There are two kinds of permutations. A “bad” permutation is one in which a number appears in its original position. A “good” permutation has no number in its original position. The following SAS/IML statements generate three random permutations of the numbers 110. The first permutation is “bad” because the number 4 is in the 4th position and the number 7 is in the 7th position. The second permutation is also bad. The third permutation is good because no number is in its original position.
proc iml;call randseed;do i = 1 to 3; perm = ranperm; print perm;end;
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Draw One Side Of The Brim
Now lets draw one side of the brim of the cowboy hat. We will begin by drawing the brim on the cowboys right side, which will be our left side. From the front of the brim, sketch a curved line that angles toward the lower part of the crown.
Now sketch a straight line from the lower part of the crown to outermost curve. This line helps to establish a bend in the brim of the hat.
Now, sketch another line parallel to and following the contours of the side of the brim. This line is for the outer seam that goes all around the brim of the hat. Extend this line to the front of the brim as well, on our rhombus shape.
Draw The Outline For The Crown And Hat Band
Well want to start off by drawing the crown and the hat band. Im using an HB pencil to begin with.
Lightly sketch a vertical line with a slight curve. This will be the front of the crown of the hat.
The top of the crown of the cowboy hat is kind of folded and bent inward. Although we dont see the view of the cowboy hat from above, we should represent this fold as we get to the top of this line. Thats why I am bending this line to form a hook which is the fold on one side and sketching a line underneath to be the other side of the top fold.
Keep extending this line in a diagonal fashion for the top of the hat. This cowboys head is tilted downward, so we dont want a perfectly horizontal line. Then curve this line downward for the back of the crown.
Sketch a line along the base of the crown that is roughly parallel to the top line. This line should have an ever so slight curve to it. This line should also connect the front and back of the crown.
Now lets sketch a somewhat rectangular outline for the hat band. This should be close to the base of the crown and following the contours of the lower edge. When we draw the brim later on, it will conceal the back of the band, so it is not necessary to go all the way back.
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How To Draw Anime Cowboy Hat Step By Step
The cowboy hat is often worn by anime characters as parts of costumes but some characters have it as a normal part of their outfit.
First draw a basic outline of the head and hair.
Draw the bottom of the top part of the hat with a large curve. This will make the hat look like its slightly pushed down on the forehead . The top part of the head should also be wider towards the bottom and narrower as it goes up. The very top of the hat should have a bit of an indent at the middle where the hat curves slightly downwards.
Draw the brim of the cowboy hat with its overall shape similar to a sausage where the ends on each side curved upwards.
Once done drawing the main shape of the hat erase the parts of the head and hair that are covered by it.
For some basic details add a wave like shape just below the top of the hat to better show that that part is slightly folded downwards. You can also add another line that traces the outline of the brim. This line can represent stitches that these hats tend to have in that area. Draw it some distance away from the brim at the front and closer to it as it progresses towards the back finally merging the two lines.
Finish the drawing by adding the details of the hair.
You can see the cowboy hat with some basic hair shading in the example above.
How To Draw A Girl Wearing A Hat Step By Step
Here is how to draw a girl or lady or woman wearing a hat. You can learn by drawing along while watching the video, or simply using the pictures to practice. Its not hard to draw a hat on a person. With this easy step by step tutorial, youll be able to draw a hat on a head soon. Just practice by drawing along.
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Draw The Front Of The Brim
Now lets look at drawing the brim. For the front part of the brim of the cowboy hat, we can draw what from this angle will look like a rhombus shape.
Begin by sketching a line going down at an angle from the front lower base of the crown.
Then, from the bottom of this line, sketch another line going to the right. This line should be roughly parallel to the base of the crown.
Finally, sketch a third line going from the last line to approximately the center of the crown base. This line should be parallel to the first one you drew. You should end up with what looks like a diamond or rhombus shape.
Animated Drawing Is A Favorite Among Young And Old
Find this pin and more on drawing by carol lumsden. Here is a fantastic anime & The first thing to remember is that chibi always have a disproportionately large head and small body. You could draw your chibi sitting down or create a simple chibi. Ideally, the ratio between the body and the head should be 1:1 or 1:4, the head being the bigger part, and the legs being distinctively short. For this step leave out all of the small splits and folds and instead draw the larger main shapes that define this particular hairstyle. Then, draw two additional curved lines that overlap. The most important thing is to hold your pencil correctly, and then you're taught a few drills to practice to improve your drawing. Extend each line using a curved line. The characters, landscapes and story lines of manga comics are emotional, adventurous and highly stylized. draw its big face and stomach which makes it look cute also. This drawing lesson will break down the instructions into easy steps. Learn how to draw cartoons, manga characters, people, animals and much more.
How To Draw A Hat Anime – Learn How To Sketch Draw 50 Free Basic Drawing For Beginners. Blake shelton belongs to usa and by profession, he is a singer. how to draw a piggy bank. draw the lines and curves forming the fur style figure below the hat and the on the edge of its cone shape. Follow along with us and learn how to draw a funny cartoon piggy bank! Drawing cartoon animals, drawing pets tagged:
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How To Draw Anime Baseball Cap Step By Step
Start by drawing an outline of the head and the estimated volume of the hair underneath the hat as shown int he above example. Draw the baseball cap over top of these to get its correct placement on the head.
Draw the top part of the cap close in shape to the outline of the hair but slightly farther away from it on top then on the sides. Draw the bill curving up around the forehead area.
After you draw the main shape of the hat erase the parts of the head and hair outline that should be hidden by it.
Next add the smaller details to the hat. As anime hats are often simplified compared to real hats you really just need to add a few small touches. In this case simply add a line tracing the outline of the bill to show the stitching that baseball caps usually have around that area. Next add a few lines going from the edges of the bill up along the sides of the hat to show the splits in the different panels baseball caps are usually made up of.
You can see a larger drawing of the finished hat along with some basic hair shading above.
How To Draw A Cartoon Cowboy Hat Using Perfect Curved Lines
In this tutorial, I will show you how to draw a nice cartoon cowboy hat! You don’t need to be a ranch worker or riding a horse in a rodeo to own a famous cowboy hat.;
This particular object is visually fascinating! So let’s try to draw a simple cowboy hat in order to understand why it is so popular! You can start with the video lesson below. The written tutorial can be found after the video. 🙂
Draw a rectangle to illustrate the crown of your hat. Notice that this shape is almost the one of a square.
Next, add a triangle just like shown above to create the rolled part of the hat.
Complete this step by drawing a rectangle in front and a circle on the far side.
Refine the outline of the crown and add a crease on top of your cowboy hat.
You can also refine the front part of the object by joining the rectangle and the circle together.
Finish the sketching part by working on your triangle. Your hat should look fine by now.
Draw some details like the hatband near the bottom of the crown. You can also add a few lines to add a realistic touch to your artwork.
Color your hat with a brown tone and paint the hatband using a color similar to the one of the skin.
Of course, you can add some shadows on your object to make this one more appealing. Great! You’ve just created a perfect cowboy hat using a few shapes and your drawing abilities! I hope you had fun drawing this particular object and don’t forget to practice!
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How To Draw A Cowboy Hat Video Tutorial
You can watch the time-lapse video version of this tutorial below. Watch it once all the way through to get a sense of the overall process. Then watch a second time and draw along with me, pausing as needed.
If you prefer, you can use one of the links directly below the video to access the complete version of this tutorial. It will show you my process for how to draw a cowboy hat step by step with video clips at normal speed.
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