Inspired by Ashish Sacheti

Probability Level 2

Two 6-sided fair dice are rolled together. Let P ( n ) P(n) denotes the probability of obtaining a product of n n . What is the relationship between P ( 16 ) P(16) and P ( 18 ) P(18) ?

Inspiration, see solution .

P ( 18 ) < P ( 16 ) P(18) < P(16) P ( 18 ) = P ( 16 ) P (18) = P(16) P ( 18 ) > P ( 16 ) P(18) > P(16)

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Calvin Lin by Calvin Lin

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1 solution

Michael Mendrin
Aug 15, 2016

4 × 4 = 16 4\times4=16 while 3 × 6 = 18 3\times6=18 . But only 1 1 out of 36 36 possible outcomes is ( 4 , 4 ) (4,4) , while 2 2 is ( 3 , 6 ) (3,6) . Hence P ( 18 ) > P ( 16 ) P(18)>P(16) .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

use \times for times instead of x

Wen Z - 4 years, 10 months ago

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there you go, fixed

Michael Mendrin - 4 years, 10 months ago

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