Question 6 (Multiple Choice, Worth 2 Points)

Carrie flipped a fair coin twice, 240 times, and recorded the results in the table.

\begin{tabular}{|l|l|l|l|l|}
\hline
Outcome & Heads, Heads & Heads, Tails & Tails, Heads & Tails, Tails \\
\hline
Frequency & 60 & 73 & 63 & 44 \\
\hline
\end{tabular}

If the coin is flipped 240 times, determine [tex]$P$[/tex] (heads, tails).

A. [tex]$25\%$[/tex]

B. [tex]$30.4\%$[/tex]

C. [tex]$34.6\%$[/tex]

D. [tex]$50.0\%$[/tex]



Answer :

To determine the experimental probability [tex]\( P \)[/tex] of getting the outcome "heads, tails" when flipping a fair coin twice, we need to follow these steps:

1. Identify the frequency of the desired outcome:
- The table shows that the frequency for the outcome "heads, tails" is 73.

2. Determine the total number of trials:
- The coin was flipped twice for a total of 240 trials as mentioned.

3. Calculate the probability:
- Probability is defined as the number of times the desired outcome occurs divided by the total number of trials.

[tex]\[ P(\text{heads, tails}) = \frac{\text{Frequency of heads, tails}}{\text{Total number of trials}} \][/tex]

Plugging in the numbers from the table:

[tex]\[ P(\text{heads, tails}) = \frac{73}{240} \][/tex]

4. Convert the probability to a percentage:
- To express the probability as a percentage, multiply by 100.

[tex]\[ P(\text{heads, tails}) = \left( \frac{73}{240} \right) \times 100 \][/tex]

Simplifying this expression gives us:

[tex]\[ P(\text{heads, tails}) \approx 30.4\% \][/tex]

Thus, the probability of flipping the coin twice and getting the outcome "heads, tails" is approximately [tex]\( 30.4\% \)[/tex].

Therefore, the correct answer is:
[tex]\[ \boxed{30.4\%} \][/tex]