Answer :
Let's break down the problem step by step to find how the experimental probability of choosing a Queen compares to the theoretical probability of choosing a Queen.
First, we need to understand the theoretical probability. Since the set of face cards contains 4 Jacks, 4 Queens, and 4 Kings, the total number of cards is:
[tex]\[ 4 + 4 + 4 = 12 \][/tex]
The probability of choosing a Queen from this set is the number of Queens divided by the total number of cards:
[tex]\[ \text{Theoretical Probability of Queen} = \frac{\text{Number of Queens}}{\text{Total Number of Cards}} = \frac{4}{12} = \frac{1}{3} \approx 0.3333 \][/tex]
Next, let's look at the experimental probability. Carlie chooses a card 60 times, and the table shows that she observed 16 Queens. The experimental probability is the number of times a Queen is chosen divided by the total number of draws:
[tex]\[ \text{Experimental Probability of Queen} = \frac{\text{Observed Queens}}{\text{Total Draws}} = \frac{16}{60} = \frac{4}{15} \approx 0.2667 \][/tex]
Now, we need to compare the experimental probability with the theoretical probability. To do this, we subtract the experimental probability from the theoretical probability:
[tex]\[ \text{Difference} = \text{Theoretical Probability} - \text{Experimental Probability} \][/tex]
[tex]\[ \text{Difference} = 0.3333 - 0.2667 = 0.0666 \][/tex]
Thus, the experimental probability of choosing a Queen (0.2667) is less than the theoretical probability of choosing a Queen (0.3333) by approximately 0.0666.
To recap:
1. The theoretical probability of choosing a Queen is approximately 0.3333.
2. The experimental probability of choosing a Queen is approximately 0.2667.
3. The difference between the theoretical and experimental probabilities is approximately 0.0666.
First, we need to understand the theoretical probability. Since the set of face cards contains 4 Jacks, 4 Queens, and 4 Kings, the total number of cards is:
[tex]\[ 4 + 4 + 4 = 12 \][/tex]
The probability of choosing a Queen from this set is the number of Queens divided by the total number of cards:
[tex]\[ \text{Theoretical Probability of Queen} = \frac{\text{Number of Queens}}{\text{Total Number of Cards}} = \frac{4}{12} = \frac{1}{3} \approx 0.3333 \][/tex]
Next, let's look at the experimental probability. Carlie chooses a card 60 times, and the table shows that she observed 16 Queens. The experimental probability is the number of times a Queen is chosen divided by the total number of draws:
[tex]\[ \text{Experimental Probability of Queen} = \frac{\text{Observed Queens}}{\text{Total Draws}} = \frac{16}{60} = \frac{4}{15} \approx 0.2667 \][/tex]
Now, we need to compare the experimental probability with the theoretical probability. To do this, we subtract the experimental probability from the theoretical probability:
[tex]\[ \text{Difference} = \text{Theoretical Probability} - \text{Experimental Probability} \][/tex]
[tex]\[ \text{Difference} = 0.3333 - 0.2667 = 0.0666 \][/tex]
Thus, the experimental probability of choosing a Queen (0.2667) is less than the theoretical probability of choosing a Queen (0.3333) by approximately 0.0666.
To recap:
1. The theoretical probability of choosing a Queen is approximately 0.3333.
2. The experimental probability of choosing a Queen is approximately 0.2667.
3. The difference between the theoretical and experimental probabilities is approximately 0.0666.