Apparently if there are 45 people in a room with you, the chance that two of them share their birthdays is 95%. Hard to believe, but who’s to argue with this? –

People = 0 Probability = 0.0

People = 1 Probability = 0.002739726027397249

People = 2 Probability = 0.008204165884781345

People = 3 Probability = 0.016355912466550326

People = 4 Probability = 0.02713557369979358

People = 5 Probability = 0.040462483649111536

People = 6 Probability = 0.056235703095975365

People = 7 Probability = 0.07433529235166902

People = 8 Probability = 0.09462383388916673

People = 9 Probability = 0.11694817771107757

People = 10 Probability = 0.141141378321733

People = 11 Probability = 0.16702478883806438

People = 12 Probability = 0.19441027523242949

People = 13 Probability = 0.223102512004973

People = 14 Probability = 0.25290131976368646

People = 15 Probability = 0.28360400525285

People = 16 Probability = 0.31500766529656066

People = 17 Probability = 0.34691141787178936

People = 18 Probability = 0.3791185260315366

People = 19 Probability = 0.41143838358058005

People = 20 Probability = 0.4436883351652058

People = 21 Probability = 0.4756953076625502

People = 22 Probability = 0.5072972343239854

People = 23 Probability = 0.5383442579145288

People = 24 Probability = 0.5686997039694639

People = 25 Probability = 0.598240820135939

People = 26 Probability = 0.626859282263242

People = 27 Probability = 0.6544614723423994

People = 28 Probability = 0.680968537477777

People = 29 Probability = 0.7063162427192686

People = 30 Probability = 0.7304546337286437

People = 31 Probability = 0.7533475278503207

People = 32 Probability = 0.774971854175772

People = 33 Probability = 0.7953168646201543

People = 34 Probability = 0.8143832388747152

People = 35 Probability = 0.8321821063798795

People = 36 Probability = 0.8487340082163846

People = 37 Probability = 0.8640678210821209

People = 38 Probability = 0.878219664366722

People = 39 Probability = 0.891231809817949

People = 40 Probability = 0.9031516114817354

People = 41 Probability = 0.9140304715618692

People = 42 Probability = 0.9239228556561199

People = 43 Probability = 0.9328853685514263

People = 44 Probability = 0.9409758994657749

People = 45 Probability = 0.9482528433672547

People = 46 Probability = 0.9547744028332993

People = 47 Probability = 0.9605979728794224

People = 48 Probability = 0.9657796093226765

People = 49 Probability = 0.9703735795779884

People = 50 Probability = 0.9744319933344283

People = 51 Probability = 0.9780045093342753

People = 52 Probability = 0.9811381134839128

People = 53 Probability = 0.9838769627588515

People = 54 Probability = 0.9862622888164461

People = 55 Probability = 0.9883323548852008

People = 56 Probability = 0.9901224593411699

People = 57 Probability = 0.9916649793892612

People = 58 Probability = 0.992989448417817

People = 59 Probability = 0.994122660865348

People = 60 Probability = 0.9950887988052908

People = 61 Probability = 0.9959095748953655

People = 62 Probability = 0.9966043868309472

People = 63 Probability = 0.9971904789669755

People = 64 Probability = 0.9976831073124921

People = 65 Probability = 0.9980957046404045

People = 66 Probability = 0.9984400429793998

People = 67 Probability = 0.9987263912544141

People = 68 Probability = 0.9989636663083863

People = 69 Probability = 0.9991595759651571

People = 70 Probability = 0.9993207531773187

People = 71 Probability = 0.9994528806414568

People = 72 Probability = 0.9995608055560187

People = 73 Probability = 0.9996486444448149

People = 74 Probability = 0.9997198781738114

People = 75 Probability = 0.9997774374531652

People = 76 Probability = 0.999823779243739

People = 77 Probability = 0.9998609545813611

People = 78 Probability = 0.9998906683968511

People = 79 Probability = 0.9999143319493135

People = 80 Probability = 0.999933108508368

People = 81 Probability = 0.9999479529215796

People = 82 Probability = 0.9999596456898823

People = 83 Probability = 0.9999688221494433

People = 84 Probability = 0.9999759973260097

People = 85 Probability = 0.9999815869898157

People = 86 Probability = 0.9999859253976947

People = 87 Probability = 0.9999892801659155

People = 88 Probability = 0.9999918646738591

People = 89 Probability = 0.9999938483561236

People = 90 Probability = 0.9999953651998191

People = 91 Probability = 0.9999965207253437

People = 92 Probability = 0.9999973976932023

People = 93 Probability = 0.9999980607467152

People = 94 Probability = 0.9999985601708488

People = 95 Probability = 0.9999989349209019

People = 96 Probability = 0.9999992150512947

People = 97 Probability = 0.9999994236541013

People = 98 Probability = 0.9999995783990275

People = 99 Probability = 0.9999996927510721

People = 100 Probability = 0.9999997769288606

People = 101 Probability = 0.9999998386553951

People = 102 Probability = 0.9999998837434765

People = 103 Probability = 0.9999999165501119

People = 104 Probability = 0.9999999403276142

People = 105 Probability = 0.999999957493643

People = 106 Probability = 0.9999999698379549

People = 107 Probability = 0.9999999786799791

People = 108 Probability = 0.9999999849883688

People = 109 Probability = 0.9999999894712943

People = 110 Probability = 0.9999999926443289

People = 111 Probability = 0.999999994881259

People = 112 Probability = 0.9999999964519412

People = 113 Probability = 0.9999999975503813

People = 114 Probability = 0.9999999983154677

People = 115 Probability = 0.9999999988462107

People = 116 Probability = 0.9999999992128945

People = 117 Probability = 0.9999999994651996

People = 118 Probability = 0.9999999996380939

People = 119 Probability = 0.9999999997560852

People = 120 Probability = 1.0