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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?

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\frac{1}{6}

\frac{1}{5}

\frac{1}{4}

\frac{1}{3}

answer is A.

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Detailed Solution

Given,
Cube is numbered from 1 to 6 and there are two cubes.
Thus, the total possible outcomes in this case
= (6×6)
=36
Total outcomes can be shown as,

\begin{matrix} (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) \\ (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) \\ (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) \\ (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) \\ (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) \\ (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) \end{matrix}

No. of favorable outcomes in which top face will have same number,

= 6 ((1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6))

Now,
Probability

P = \frac{(No . of favorable outcomes)}{(Total no . of possible outcomes)}

For our case,
P

= \frac{6}{36}

P = \frac{1}{6}

Option 1 is correct.
[w1]Not checking as plagiarism is more than 30%
[w2]Not checking as plagiarism is more than 30%
Plagiarism is 67%.

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