Calculate the change that there are peopele with the same birthday.

![plot](./plot.svg)

| group size | chance in fraction |
|----|-----------------------|
| 2  | 0.0027397260273972603 |
| 3  | 0.008204165884781385  |
| 4  | 0.016355912466550306  |
| 5  | 0.027135573699793587  |
| 6  | 0.04046248364911148   |
| 7  | 0.0562357030959754    |
| 8  | 0.07433529235166902   |
| 9  | 0.09462383388916669   |
| 10 | 0.11694817771107764   |
| 11 | 0.14114137832173304   |
| 12 | 0.16702478883806438   |
| 13 | 0.19441027523242937   |
| 14 | 0.223102512004973     |
| 15 | 0.25290131976368635   |
| 16 | 0.2836040052528499    |
| 17 | 0.3150076652965606    |
| 18 | 0.3469114178717893    |
| 19 | 0.3791185260315367    |
| 20 | 0.41143838358058      |
| 21 | 0.4436883351652057    |
| 22 | 0.4756953076625501    |
| 23 | 0.5072972343239854    |
| 24 | 0.5383442579145288    |
| 25 | 0.5686997039694639    |
| 26 | 0.5982408201359389    |
| 27 | 0.626859282263242     |
| 28 | 0.6544614723423994    |
| 29 | 0.680968537477777     |
| 30 | 0.7063162427192686    |
| 31 | 0.7304546337286438    |
| 32 | 0.7533475278503207    |
| 33 | 0.774971854175772     |
| 34 | 0.7953168646201543    |
| 35 | 0.8143832388747152    |
| 36 | 0.8321821063798795    |
| 37 | 0.8487340082163846    |
| 38 | 0.8640678210821209    |
| 39 | 0.8782196643667219    |
| 40 | 0.8912318098179489    |
| 41 | 0.9031516114817353    |
| 42 | 0.9140304715618691    |
| 43 | 0.9239228556561198    |
| 44 | 0.9328853685514262    |
| 45 | 0.9409758994657749    |
| 46 | 0.9482528433672547    |
| 47 | 0.9547744028332993    |
| 48 | 0.9605979728794224    |
| 49 | 0.9657796093226765    |
| 50 | 0.9703735795779884    |
| 51 | 0.9744319933344283    |
| 52 | 0.9780045093342753    |
| 53 | 0.9811381134839128    |
| 54 | 0.9838769627588515    |
| 55 | 0.9862622888164461    |
| 56 | 0.9883323548852008    |
| 57 | 0.9901224593411699    |
| 58 | 0.9916649793892612    |
| 59 | 0.992989448417817     |
| 60 | 0.994122660865348     |
| 61 | 0.9950887988052908    |
| 62 | 0.9959095748953655    |
| 63 | 0.9966043868309472    |
| 64 | 0.9971904789669755    |
| 65 | 0.9976831073124922    |
| 66 | 0.9980957046404045    |
| 67 | 0.9984400429793999    |
| 68 | 0.9987263912544142    |
| 69 | 0.9989636663083864    |
| 70 | 0.9991595759651571    |