Answer :
To determine the probability [tex]\( P \)[/tex] of getting tails, tails (Tails, Tails) based on the recorded outcomes when a fair coin is flipped twice for a total of 240 times, we need to follow these steps:
1. Identify the total number of trials (flips):
According to the problem, the total number of times Carrie flipped the coin twice is 240.
2. Identify the frequency of the specific outcome (tails, tails):
From the table provided, the frequency of getting tails, tails is 44.
3. Calculate the probability:
The probability [tex]\( P \)[/tex] of an event is given by the ratio of the number of successful outcomes to the total number of trials. In this case, it can be written as:
[tex]\[ P(\text{Tails, Tails}) = \frac{\text{Number of Tails, Tails Outcomes}}{\text{Total Number of Trials}} \][/tex]
Plugging the numbers in:
[tex]\[ P(\text{Tails, Tails}) = \frac{44}{240} \][/tex]
4. Convert the probability to a percentage:
To express the probability as a percentage, we multiply it by 100:
[tex]\[ P(\text{Tails, Tails}) \times 100 = \left( \frac{44}{240} \right) \times 100 \approx 18.33\% \][/tex]
Thus, the probability [tex]\( P \)[/tex] of getting tails, tails when the coin is flipped twice 240 times is approximately [tex]\( 18.33\% \)[/tex].
Comparing this result to the given options:
- [tex]\( 18.3 \% \)[/tex]
- [tex]\( 25 \% \)[/tex]
- [tex]\( 44.8 \% \)[/tex]
- [tex]\( 50.0 \% \)[/tex]
We can see that the closest match is [tex]\( \mathbf{18.3\%} \)[/tex].
Therefore, the correct answer is [tex]\( \boxed{18.3\%} \)[/tex].
1. Identify the total number of trials (flips):
According to the problem, the total number of times Carrie flipped the coin twice is 240.
2. Identify the frequency of the specific outcome (tails, tails):
From the table provided, the frequency of getting tails, tails is 44.
3. Calculate the probability:
The probability [tex]\( P \)[/tex] of an event is given by the ratio of the number of successful outcomes to the total number of trials. In this case, it can be written as:
[tex]\[ P(\text{Tails, Tails}) = \frac{\text{Number of Tails, Tails Outcomes}}{\text{Total Number of Trials}} \][/tex]
Plugging the numbers in:
[tex]\[ P(\text{Tails, Tails}) = \frac{44}{240} \][/tex]
4. Convert the probability to a percentage:
To express the probability as a percentage, we multiply it by 100:
[tex]\[ P(\text{Tails, Tails}) \times 100 = \left( \frac{44}{240} \right) \times 100 \approx 18.33\% \][/tex]
Thus, the probability [tex]\( P \)[/tex] of getting tails, tails when the coin is flipped twice 240 times is approximately [tex]\( 18.33\% \)[/tex].
Comparing this result to the given options:
- [tex]\( 18.3 \% \)[/tex]
- [tex]\( 25 \% \)[/tex]
- [tex]\( 44.8 \% \)[/tex]
- [tex]\( 50.0 \% \)[/tex]
We can see that the closest match is [tex]\( \mathbf{18.3\%} \)[/tex].
Therefore, the correct answer is [tex]\( \boxed{18.3\%} \)[/tex].
