Question

In: Statistics and Probability

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

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!

orchestra answered 1 year ago

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