Question

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?

Answer 1

Hint: Find the total number of outcomes and also find the number where we get the same number on both cubes.

Complete step-by-step answer:
In a throw of pair of cubes, yellow and red, total no of possible outcomes = 36 (\[6 \times 6\])
Which are,
\[
  \{ (1,1)(1,2)(1,3)(1,4)(1,5),(1,6), \\
  (2,1)(2,2)(2,3)(2,4)(2,5),(2,6), \\
  (3,1)(3,2)(3,3)(3,4)(3,5),(3,6), \\
  (4,1)(4,2)(4,3)(4,4)(4,5),(4,6), \\
  (5,1)(5,2)(5,3)(5,4)(5,5),(5,6), \\
  (6,1)(6,2)(6,3)(6,4)(6,5),(6,6)\} \\
\]
Let E be the event of getting the same number on both cubes,
No. of favorable outcomes = 6
We know the probability P(E) = (no. of favorable outcomes)/ ( Total no. of possible outcomes) = \[\dfrac{6}{{36}} = \dfrac{1}{6}\]
Therefore, the probability that the top face of each cube will have the same number = \[\dfrac{1}{6}\]

Note: The colors are only given to confuse you from your desired result. Don’t pay any attention to that.
Always first make a Sample Space of the total number of possible outcomes, and from that we can get the no. of favorable outcomes.