The faces of a red cube and a yellow cube are numbered from 1 to 6. Both cubes are rolled. What is the probability that the top face of each cube will have the same number?

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Solution

The possible outcomes of the same number={(1,1)(2,2)(3,3)(4,4)(5,5)(6,6)}

$\to$ Total number=6

The dice/cubes can appear in 36 different ways $\to$ 6 $\times$ 6

Of these, 6 pairs are doubles...

$\frac{6}{36}$ = $\frac{1}{6}$

Hence the probability that the top face of each cube will have the same number is $\frac{1}{6}$

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The faces of a red cube and a yellow cube are numbered from 1 to 6. Both cubes are rolled. What is the probability that the top face of each cube will have the same number?

The possible outcomes of the same number={(1,1)(2,2)(3,3)(4,4)(5,5)(6,6)} → Total number=6 The dice/cubes can appear in 36 different ways → 6 × 6 Of these, 6 pairs are doubles... 636 = 16 Hence the probability that the top face of each cube will have the same number is 16