Rolling four die

Probability Level pending

Ruby McTube has four six sided die.

They each have the following numbers on their six faces: 1 , 1 , 2 , 2 , 4 , 6 1,1,2,2,4,6

If she rolls all four, the probability they each show a different number on top is a b \frac{a}{b} where a a and b b are coprime positive integers.

What is a + b a+b ?


Image credit: http://wherethewindsblow.com/


The answer is 29.

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1 solution

Geoff Pilling
Aug 17, 2016

For a given combination (i.e. First die = 1 =1 , Second die = 2 =2 , Third die = 4 =4 , Fourth die = 6 =6 ) the probability of getting this combination is 1 3 × 1 3 × 1 6 × 1 6 \frac{1}{3} \times \frac{1}{3} \times \frac{1}{6} \times \frac{1}{6}

And there are 4 ! = 24 4! = 24 such combinations.

So, the probability they are all different = 24 × 1 3 × 1 3 × 1 6 × 1 6 = 2 27 = 24 \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{6} \times \frac{1}{6} = \frac{2}{27}

2 + 27 = 29 2+27 = \boxed{29}

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