Question

In: Statistics and Probability

are the outcomes of three rolled dice equally likely

are the outcomes of three rolled dice equally likely




Solutions

Expert Solution

For a fair dice, YES the outcomes of a three rolled dice are equally likely.

There are a total of outcomes possible, and each one of these outcomes has the same probability 1/216 of occurring.

The list of the outcomes are:

Outcome1: 1 1 ,1
Outcome2: 1 ,1 ,2
Outcome3: 1 ,1 ,3
Outcome4: 1 ,1 ,4
Outcome5: 1 ,1 ,5
Outcome6: 1 ,1 ,6
Outcome7: 1 ,2 ,1
Outcome8: 1 ,2 ,2
Outcome9: 1 ,2 ,3
Outcome10: 1 ,2 ,4
Outcome11: 1 ,2 ,5
Outcome12: 1 ,2 ,6
Outcome13: 1 ,3 ,1
Outcome14: 1 ,3 ,2
Outcome15: 1 ,3 ,3
Outcome16: 1 ,3 ,4
Outcome17: 1 ,3 ,5
Outcome18: 1 ,3 ,6
Outcome19: 1 ,4 ,1
Outcome20: 1 ,4 ,2
Outcome21: 1 ,4 ,3
Outcome22: 1 ,4 ,4
Outcome23: 1 ,4 ,5
Outcome24: 1 ,4 ,6
Outcome25: 1 ,5 ,1
Outcome26: 1 ,5 ,2
Outcome27: 1 ,5 ,3
Outcome28: 1 ,5 ,4
Outcome29: 1 ,5 ,5
Outcome30: 1 ,5 ,6
Outcome31: 1 ,6 ,1
Outcome32: 1 ,6 ,2
Outcome33: 1 ,6 ,3
Outcome34: 1 ,6 ,4
Outcome35: 1 ,6 ,5
Outcome36: 1 ,6 ,6
Outcome37: 2 ,1 ,1
Outcome38: 2 ,1 ,2
Outcome39: 2 ,1 ,3
Outcome40: 2 ,1 ,4
Outcome41: 2 ,1 ,5
Outcome42: 2 ,1 ,6
Outcome43: 2 ,2 ,1
Outcome44: 2 ,2 ,2
Outcome45: 2 ,2 ,3
Outcome46: 2 ,2 ,4
Outcome47: 2 ,2 ,5
Outcome48: 2 ,2 ,6
Outcome49: 2 ,3 ,1
Outcome50: 2 ,3 ,2
Outcome51: 2 ,3 ,3
Outcome52: 2 ,3 ,4
Outcome53: 2 ,3 ,5
Outcome54: 2 ,3 ,6
Outcome55: 2 ,4 ,1
Outcome56: 2 ,4 ,2
Outcome57: 2 ,4 ,3
Outcome58: 2 ,4 ,4
Outcome59: 2 ,4 ,5
Outcome60: 2 ,4 ,6
Outcome61: 2 ,5 ,1
Outcome62: 2 ,5 ,2
Outcome63: 2 ,5 ,3
Outcome64: 2 ,5 ,4
Outcome65: 2 ,5 ,5
Outcome66: 2 ,5 ,6
Outcome67: 2 ,6 ,1
Outcome68: 2 ,6 ,2
Outcome69: 2 ,6 ,3
Outcome70: 2 ,6 ,4
Outcome71: 2 ,6 ,5
Outcome72: 2 ,6 ,6
Outcome73: 3 ,1 ,1
Outcome74: 3 ,1 ,2
Outcome75: 3 ,1 ,3
Outcome76: 3 ,1 ,4
Outcome77: 3 ,1 ,5
Outcome78: 3 ,1 ,6
Outcome79: 3 ,2 ,1
Outcome80: 3 ,2 ,2
Outcome81: 3 ,2 ,3
Outcome82: 3 ,2 ,4
Outcome83: 3 ,2 ,5
Outcome84: 3 ,2 ,6
Outcome85: 3 ,3 ,1
Outcome86: 3 ,3 ,2
Outcome87: 3 ,3 ,3
Outcome88: 3 ,3 ,4
Outcome89: 3 ,3 ,5
Outcome90: 3 ,3 ,6
Outcome91: 3 ,4 ,1
Outcome92: 3 ,4 ,2
Outcome93: 3 ,4 ,3
Outcome94: 3 ,4 ,4
Outcome95: 3 ,4 ,5
Outcome96: 3 ,4 ,6
Outcome97: 3 ,5 ,1
Outcome98: 3 ,5 ,2
Outcome99: 3 ,5 ,3
Outcome100: 3 ,5 ,4
Outcome101: 3 ,5 ,5
Outcome102: 3 ,5 ,6
Outcome103: 3 ,6 ,1
Outcome104: 3 ,6 ,2
Outcome105: 3 ,6 ,3
Outcome106: 3 ,6 ,4
Outcome107: 3 ,6 ,5
Outcome108: 3 ,6 ,6
Outcome109: 4 ,1 ,1
Outcome110: 4 ,1 ,2
Outcome111: 4 ,1 ,3
Outcome112: 4 ,1 ,4
Outcome113: 4 ,1 ,5
Outcome114: 4 ,1 ,6
Outcome115: 4 ,2 ,1
Outcome116: 4 ,2 ,2
Outcome117: 4 ,2 ,3
Outcome118: 4 ,2 ,4
Outcome119: 4 ,2 ,5
Outcome120: 4 ,2 ,6
Outcome121: 4 ,3 ,1
Outcome122: 4 ,3 ,2
Outcome123: 4 ,3 ,3
Outcome124: 4 ,3 ,4
Outcome125: 4 ,3 ,5
Outcome126: 4 ,3 ,6
Outcome127: 4 ,4 ,1
Outcome128: 4 ,4 ,2
Outcome129: 4 ,4 ,3
Outcome130: 4 ,4 ,4
Outcome131: 4 ,4 ,5
Outcome132: 4 ,4 ,6
Outcome133: 4 ,5 ,1
Outcome134: 4 ,5 ,2
Outcome135: 4 ,5 ,3
Outcome136: 4 ,5 ,4
Outcome137: 4 ,5 ,5
Outcome138: 4 ,5 ,6
Outcome139: 4 ,6 ,1
Outcome140: 4 ,6 ,2
Outcome141: 4 ,6 ,3
Outcome142: 4 ,6 ,4
Outcome143: 4 ,6 ,5
Outcome144: 4 ,6 ,6
Outcome145: 5 ,1 ,1
Outcome146: 5 ,1 ,2
Outcome147: 5 ,1 ,3
Outcome148: 5 ,1 ,4
Outcome149: 5 ,1 ,5
Outcome150: 5 ,1 ,6
Outcome151: 5 ,2 ,1
Outcome152: 5 ,2 ,2
Outcome153: 5 ,2 ,3
Outcome154: 5 ,2 ,4
Outcome155: 5 ,2 ,5
Outcome156: 5 ,2 ,6
Outcome157: 5 ,3 ,1
Outcome158: 5 ,3 ,2
Outcome159: 5 ,3 ,3
Outcome160: 5 ,3 ,4
Outcome161: 5 ,3 ,5
Outcome162: 5 ,3 ,6
Outcome163: 5 ,4 ,1
Outcome164: 5 ,4 ,2
Outcome165: 5 ,4 ,3
Outcome166: 5 ,4 ,4
Outcome167: 5 ,4 ,5
Outcome168: 5 ,4 ,6
Outcome169: 5 ,5 ,1
Outcome170: 5 ,5 ,2
Outcome171: 5 ,5 ,3
Outcome172: 5 ,5 ,4
Outcome173: 5 ,5 ,5
Outcome174: 5 ,5 ,6
Outcome175: 5 ,6 ,1
Outcome176: 5 ,6 ,2
Outcome177: 5 ,6 ,3
Outcome178: 5 ,6 ,4
Outcome179: 5 ,6 ,5
Outcome180: 5 ,6 ,6
Outcome181: 6 ,1 ,1
Outcome182: 6 ,1 ,2
Outcome183: 6 ,1 ,3
Outcome184: 6 ,1 ,4
Outcome185: 6 ,1 ,5
Outcome186: 6 ,1 ,6
Outcome187: 6 ,2 ,1
Outcome188: 6 ,2 ,2
Outcome189: 6 ,2 ,3
Outcome190: 6 ,2 ,4
Outcome191: 6 ,2 ,5
Outcome192: 6 ,2 ,6
Outcome193: 6 ,3 ,1
Outcome194: 6 ,3 ,2
Outcome195: 6 ,3 ,3
Outcome196: 6 ,3 ,4
Outcome197: 6 ,3 ,5
Outcome198: 6 ,3 ,6
Outcome199: 6 ,4 ,1
Outcome200: 6 ,4 ,2
Outcome201: 6 ,4 ,3
Outcome202: 6 ,4 ,4
Outcome203: 6 ,4 ,5
Outcome204: 6 ,4 ,6
Outcome205: 6 ,5 ,1
Outcome206: 6 ,5 ,2
Outcome207: 6 ,5 ,3
Outcome208: 6 ,5 ,4
Outcome209: 6 ,5 ,5
Outcome210: 6 ,5 ,6
Outcome211: 6 ,6 ,1
Outcome212: 6 ,6 ,2
Outcome213: 6 ,6 ,3
Outcome214: 6 ,6 ,4
Outcome215: 6 ,6 ,5
Outcome216: 6 ,6 ,6

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