Answer :
Sure, let's break down the problem step-by-step.
### Step 1: Probability of Spinning a Red or Green
1. Assume a spinner with equal sections for red, green, and other colors.
2. Let’s consider there is 1 section each for red and green, and 2 sections for other colors.
- Number of red sections = 1
- Number of green sections = 1
- Number of other sections = 2
3. The total number of sections = 1 (red) + 1 (green) + 2 (other) = 4
4. The probability of spinning a red or green is calculated as follows:
- [tex]\( P(\text{Red or Green}) = \frac{\text{Number of Red sections} + \text{Number of Green sections}}{\text{Total sections}} \)[/tex]
- [tex]\( P(\text{Red or Green}) = \frac{1 + 1}{4} = \frac{2}{4} = 0.5 \)[/tex]
### Step 2: Probability of Rolling a Number Greater than 4
1. Consider a standard 6-sided die with numbers 1 through 6.
2. Numbers greater than 4 on the die are 5 and 6.
- Number of favorable outcomes (greater than 4) = 2 (numbers 5 and 6)
3. Total number of outcomes on a 6-sided die = 6
4. The probability of rolling a number greater than 4 is:
- [tex]\( P(\text{>4}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of sides}} \)[/tex]
- [tex]\( P(\text{>4}) = \frac{2}{6} = \frac{1}{3} \approx 0.3333 \)[/tex]
### Step 3: Combined Probability of Both Events Happening
1. These two events (spinning a red or green and rolling a number greater than 4) are independent.
2. The probability of both events occurring is the product of their individual probabilities:
- [tex]\( P(\text{Both Events}) = P(\text{Red or Green}) \times P(\text{>4}) \)[/tex]
- [tex]\( P(\text{Both Events}) = 0.5 \times 0.3333 \approx 0.1667 \)[/tex]
### Summary:
- Probability of spinning a red or green: 0.5
- Probability of rolling a number greater than 4: 0.3333
- Probability of both events happening: 0.1667
So, the probability that you spin a red or green and the number cube lands on a number greater than 4 is approximately 0.1667.
### Step 1: Probability of Spinning a Red or Green
1. Assume a spinner with equal sections for red, green, and other colors.
2. Let’s consider there is 1 section each for red and green, and 2 sections for other colors.
- Number of red sections = 1
- Number of green sections = 1
- Number of other sections = 2
3. The total number of sections = 1 (red) + 1 (green) + 2 (other) = 4
4. The probability of spinning a red or green is calculated as follows:
- [tex]\( P(\text{Red or Green}) = \frac{\text{Number of Red sections} + \text{Number of Green sections}}{\text{Total sections}} \)[/tex]
- [tex]\( P(\text{Red or Green}) = \frac{1 + 1}{4} = \frac{2}{4} = 0.5 \)[/tex]
### Step 2: Probability of Rolling a Number Greater than 4
1. Consider a standard 6-sided die with numbers 1 through 6.
2. Numbers greater than 4 on the die are 5 and 6.
- Number of favorable outcomes (greater than 4) = 2 (numbers 5 and 6)
3. Total number of outcomes on a 6-sided die = 6
4. The probability of rolling a number greater than 4 is:
- [tex]\( P(\text{>4}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of sides}} \)[/tex]
- [tex]\( P(\text{>4}) = \frac{2}{6} = \frac{1}{3} \approx 0.3333 \)[/tex]
### Step 3: Combined Probability of Both Events Happening
1. These two events (spinning a red or green and rolling a number greater than 4) are independent.
2. The probability of both events occurring is the product of their individual probabilities:
- [tex]\( P(\text{Both Events}) = P(\text{Red or Green}) \times P(\text{>4}) \)[/tex]
- [tex]\( P(\text{Both Events}) = 0.5 \times 0.3333 \approx 0.1667 \)[/tex]
### Summary:
- Probability of spinning a red or green: 0.5
- Probability of rolling a number greater than 4: 0.3333
- Probability of both events happening: 0.1667
So, the probability that you spin a red or green and the number cube lands on a number greater than 4 is approximately 0.1667.
