Question

a rolling two standard number cubes and both number cubes show a 6

Explanation:

Step1: Determine total outcomes for one cube

A standard number cube has 6 faces (numbers 1 - 6), so for one cube, there are 6 possible outcomes.

Step2: Determine total outcomes for two cubes

When rolling two cubes, the total number of outcomes is the product of the number of outcomes for each cube. So, using the multiplication principle, total outcomes = \(6\times6 = 36\).

Step3: Determine favorable outcomes

The favorable outcome (both showing 6) is 1 (i.e., (6, 6)).

Step4: Calculate probability

Probability is the number of favorable outcomes divided by the total number of outcomes. So, probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{1}{36}\).

Answer:

The probability that both number cubes show a 6 is \(\frac{1}{36}\).