Question

sam and erica are playing a board game. they spin a pointer to determine whether to move forward or back. they toss a number cube to determine how many spaces to move. what is the probability of moving forward an even number of spaces? \\(\frac{1}{4}\\) \\(\frac{1}{2}\\) \\(\frac{1}{3}\\) \\(\frac{1}{6}\\)

Explanation:

Step1: Probability of moving forward

The spinner has two equal sections: "Move Forward" and "Move Back". So the probability of moving forward, \( P(\text{forward}) = \frac{1}{2} \).

Step2: Probability of even number on cube

A number cube (die) has numbers 1, 2, 3, 4, 5, 6. Even numbers are 2, 4, 6. So there are 3 even numbers out of 6. Thus, \( P(\text{even}) = \frac{3}{6} = \frac{1}{2} \).

Step3: Probability of both events

Since the two events (spinning forward and rolling even) are independent, we multiply their probabilities: \( P = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \). Wait, no—wait, let's check again. Wait, the number cube in the image shows 1, 2, 4? Wait, no, maybe the cube is a standard die? Wait, the problem says "toss a number cube"—standard die has 1 - 6. But the image shows a cube with 1, 2, 4? Wait, maybe that's a typo, but the standard approach: forward probability is 1/2 (since two equal sections). Even numbers on die: 2,4,6 (three numbers), so probability 3/6 = 1/2. Then combined probability: 1/2 1/2 = 1/4? Wait, no, wait: the question is moving forward AND even number of spaces. So independent events, so multiply. So 1/2 (forward) 1/2 (even) = 1/4? Wait, but let's confirm. Wait, the number of even numbers on a die: 2,4,6: 3 out of 6, so 1/2. Forward: 1/2. So 1/2 * 1/2 = 1/4. So the probability is 1/4.

Answer:

\(\frac{1}{4}\) (corresponding to the first option, e.g., A. \(\frac{1}{4}\) if options are labeled, but based on the calculation, the answer is \(\frac{1}{4}\))