Let's approach this question step-by-step.
### Step 1: Identify All Possible Outcomes
When flipping a penny and a dime, each coin has two possible outcomes: heads (H) or tails (T). To determine the total outcomes when flipping both, we list all possible combinations of these outcomes.
The possible outcomes are:
1. Penny: Head, Dime: Head (HH)
2. Penny: Head, Dime: Tail (HT)
3. Penny: Tail, Dime: Head (TH)
4. Penny: Tail, Dime: Tail (TT)
We can represent this in a table:
[tex]\[
\begin{tabular}{|l|l|}
\hline \text{Penny} & \text{Dime} \\
\hline \text{Head} & \text{Head} \\
\hline \text{Head} & \text{Tail} \\
\hline \text{Tail} & \text{Head} \\
\hline \text{Tail} & \text{Tail} \\
\hline
\end{tabular}
\][/tex]
### Step 2: Count the Total Number of Outcomes
There are 4 possible outcomes when flipping a penny and a dime:
1. (Head, Head)
2. (Head, Tail)
3. (Tail, Head)
4. (Tail, Tail)
So, the number of total outcomes is 4.
### Step 3: Identify the Desired Outcome
We are interested in the probability of getting two heads (HH). From the list of all possible outcomes, the combination "Head, Head" appears only once.
### Step 4: Calculate the Probability
The probability [tex]\(P\)[/tex] of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
So, the number of favorable outcomes (HH) = 1.
Hence, the probability of getting two heads is:
[tex]\[ P(\text{2 heads}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{4} \][/tex]
Expressing this as a decimal:
[tex]\[ \frac{1}{4} = 0.25 \][/tex]
### Step 5: Selecting the Correct Answer
The correct probability of getting two heads is [tex]\(0.25\)[/tex].
Comparing this with the given choices:
a. [tex]\( \frac{1}{2} \)[/tex]
b. [tex]\( \frac{3}{4} \)[/tex]
c. [tex]\( \frac{4}{4} \)[/tex]
None of these matches the numerical result of [tex]\(0.25\)[/tex]. Thus, it appears there may be a mistake in the options provided. Ideally, the correct answer in terms of the provided choices should have been an option of [tex]\(\frac{1}{4}\)[/tex].
Therefore, based on our calculations, the correct probability of getting two heads is [tex]\(0.25 \)[/tex] or [tex]\(\frac{1}{4}\)[/tex].
