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? image: a spinner split into two equal halves (green: \move forward\, red: \move back\) and a number cube showing faces 1, 2, 4. options: \\(\frac{1}{6}\\), \\(\frac{1}{4}\\), \\(\frac{1}{3}\\), \\(\frac{1}{2}\\)

Explanation:

Step1: Probability of moving forward

The spinner has two equal parts: "Move Forward" and "Move Back". So the probability of moving forward, \( P(\text{forward}) \), is the number of favorable outcomes (1, for "Move Forward") divided by the total number of outcomes (2). So \( P(\text{forward}) = \frac{1}{2} \).

Step2: Probability of even number on cube

A number cube (die) has numbers 1, 2, 3, 4, 5, 6. The even numbers are 2, 4, 6. So there are 3 favorable outcomes out of 6 total. Thus, the probability of rolling an even number, \( P(\text{even}) \), is \( \frac{3}{6} = \frac{1}{2} \).

Step3: Probability of both events

Since the two events (spinning forward and rolling an even number) are independent, we multiply their probabilities. So the combined probability \( P = P(\text{forward}) \times P(\text{even}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \).

Answer:

\(\frac{1}{4}\) (corresponding to the option \(\frac{1}{4}\))