Question

1. you roll a pair of number cubes. what is the probability of getting even numbers on both cubes? -1 -1/2 -1/3 -1/4

Explanation:

Step1: Determine the total number of outcomes

When rolling a pair of number cubes (each cube has 6 faces numbered from 1 - 6), the total number of outcomes is \(n(S)=6\times6 = 36\) (by the fundamental counting principle: if one event has \(m\) possible outcomes and another independent event has \(n\) possible outcomes, then the two - event combination has \(m\times n\) possible outcomes).

Step2: Determine the number of favorable outcomes

The even numbers on a number cube are 2, 4, 6. So, the number of ways to get an even number on the first cube is 3 (either 2, 4, or 6), and the number of ways to get an even number on the second cube is also 3. By the fundamental counting principle, the number of favorable outcomes \(n(E)=3\times3=9\).

Step3: Calculate the probability

The probability formula is \(P(E)=\frac{n(E)}{n(S)}\). Substituting \(n(E) = 9\) and \(n(S)=36\) into the formula, we get \(P(E)=\frac{9}{36}=\frac{1}{4}\).

Answer:

\(\frac{1}{4}\)