Answer :
Sure, let's break down the solution step-by-step:
1. Identify the Observed Frequency of Rolling a 3:
From the table, the observed frequency of rolling a 3 is given as 24.
2. Calculate the Total Number of Rolls:
To find the total number of rolls, we sum up the observed frequencies of all the faces of the number cube:
[tex]\[ 18 + 16 + 24 + 26 + 16 + 20 = 120 \][/tex]
3. Calculate the Experimental Probability of Rolling a 3:
The experimental probability is determined by dividing the observed frequency of rolling a 3 by the total number of rolls:
[tex]\[ \text{Experimental Probability} = \frac{\text{Observed Frequency of rolling a 3}}{\text{Total Number of Rolls}} = \frac{24}{120} = 0.2 \][/tex]
4. Determine the Theoretical Probability of Rolling a 3:
The theoretical probability is based on the assumption that the number cube is fair, meaning each face has an equal likelihood of landing face up. Since a number cube (die) has six faces, each face has a probability of:
[tex]\[ \text{Theoretical Probability} = \frac{1}{6} \approx 0.1667 \][/tex]
5. Compare the Experimental Probability with Theoretical Probability:
- The experimental probability is [tex]\(0.2\)[/tex] or 20%.
- The theoretical probability is approximately [tex]\(0.1667\)[/tex] or 16.67%.
By comparing these two probabilities, we observe that the experimental probability ([tex]\(0.2\)[/tex]) is slightly higher than the theoretical probability ([tex]\(0.1667\)[/tex]). This indicates that, in this specific experiment, the number 3 came up a bit more frequently than would be expected in theory for a fair number cube.
In summary, the experimental probability of rolling a 3 (0.2) is higher than the theoretical probability of rolling a 3 (0.1667), suggesting a slight discrepancy between observed results and theoretical expectations. This can happen due to random variation in a finite number of trials.
1. Identify the Observed Frequency of Rolling a 3:
From the table, the observed frequency of rolling a 3 is given as 24.
2. Calculate the Total Number of Rolls:
To find the total number of rolls, we sum up the observed frequencies of all the faces of the number cube:
[tex]\[ 18 + 16 + 24 + 26 + 16 + 20 = 120 \][/tex]
3. Calculate the Experimental Probability of Rolling a 3:
The experimental probability is determined by dividing the observed frequency of rolling a 3 by the total number of rolls:
[tex]\[ \text{Experimental Probability} = \frac{\text{Observed Frequency of rolling a 3}}{\text{Total Number of Rolls}} = \frac{24}{120} = 0.2 \][/tex]
4. Determine the Theoretical Probability of Rolling a 3:
The theoretical probability is based on the assumption that the number cube is fair, meaning each face has an equal likelihood of landing face up. Since a number cube (die) has six faces, each face has a probability of:
[tex]\[ \text{Theoretical Probability} = \frac{1}{6} \approx 0.1667 \][/tex]
5. Compare the Experimental Probability with Theoretical Probability:
- The experimental probability is [tex]\(0.2\)[/tex] or 20%.
- The theoretical probability is approximately [tex]\(0.1667\)[/tex] or 16.67%.
By comparing these two probabilities, we observe that the experimental probability ([tex]\(0.2\)[/tex]) is slightly higher than the theoretical probability ([tex]\(0.1667\)[/tex]). This indicates that, in this specific experiment, the number 3 came up a bit more frequently than would be expected in theory for a fair number cube.
In summary, the experimental probability of rolling a 3 (0.2) is higher than the theoretical probability of rolling a 3 (0.1667), suggesting a slight discrepancy between observed results and theoretical expectations. This can happen due to random variation in a finite number of trials.
