Sam and Eric are playing a boardgame. They spin a pointer to determine whether to move forward or back. they toss a cube to determine how many spaces to move. What is the probability of moving forward an even number of spaces
To determine the probability of moving forward an even number of spaces, we need to consider the possible outcomes for both spinning the pointer and tossing the cube.
Let's assume that the pointer has two options: "forward" or "back" and that when tossing the cube, the numbers 1, 2, 3, 4, 5, and 6 can occur with equal likelihood.
To move forward an even number of spaces, the following combinations are possible:
1. Moving forward 0 spaces (spinning "back" and tossing a 1, 3, or 5).
2. Moving forward 2 spaces (spinning "forward" and tossing a 2, 4, or 6).
3. Moving forward 4 spaces (spinning "back" and tossing a 2 or 4).
4. Moving forward 6 spaces (spinning "forward" and tossing a 6).
Out of these four favorable combinations, the total number of possible outcomes is 2 (forward or back option for the pointer) multiplied by 6 (possible numbers on the cube), which equals 12.
Therefore, the probability of moving forward an even number of spaces is 4 (favorable combinations) divided by 12 (total combinations), which simplifies to 1/3 or approximately 0.33.
To find the probability of moving forward an even number of spaces, we need to consider the possible outcomes of the pointer spin and cube toss.
1. Pointer Spin:
- There are two possible outcomes for the pointer spin: forward (F) or backward (B).
- The probability of spinning forward is 1/2, and the probability of spinning backward is also 1/2.
2. Cube Toss:
- The cube can have an even number of outcomes, such as 2, 4, or 6. These represent the number of spaces to move.
- Out of the total six possible outcomes of the cube toss (1, 2, 3, 4, 5, 6), half of them are even.
To determine the probability of moving forward an even number of spaces, we need to consider both the outcomes of the pointer spin and the cube toss.
1. When spinning forward:
- The probability of spinning forward is 1/2.
- If the cube toss results in an odd number of spaces, the player will not move forward an even number of spaces.
2. When spinning backward:
- The probability of spinning backward is 1/2.
- If the cube toss results in an even number of spaces, the player will not move forward an even number of spaces.
Since the player can only move forward an even number of spaces when spinning forward and getting an even number on the cube toss, we need to consider the probability of both events happening together.
The probability of moving forward an even number of spaces = Probability of spinning forward (1/2) * Probability of getting an even number on the cube toss (1/2)
Probability of moving forward an even number of spaces = (1/2) * (1/2) = 1/4
Therefore, the probability of moving forward an even number of spaces is 1/4 or 25%.