Questions: The results of a simulation of the event of tossing two fair coins 25 times is shown. What is the simulated probability of the outcome Π, where T represents tails. T H T T T H H T H H H H H H H T T H T T T T T T T H T H H H H T H T H T T H H H H H H H H H H H The simulated probability of the event T T is (Type an integer or decimal rounded to two decimal places as needed.)

The results of a simulation of the event of tossing two fair coins 25 times is shown. What is the simulated probability of the outcome Π, where T represents tails.

T H T T T H H T
H H H H H H H T T H
T T T T T T T H T H
H H H T H T H T T H
H H H H H H H H H H

The simulated probability of the event T T is
(Type an integer or decimal rounded to two decimal places as needed.)

Transcript text: The results of a simulation of the event of tossing two fair coins 25 times is shown. What is the simulated probability of the outcome $\Pi$, where $T$ represents tails. \begin{tabular}{|c|c|c|c|c|} \hline$T H$ & $T T$ & $T$ & $H H$ & $T$ \\ \hline$H H$ & $H H$ & $H H$ & $H T$ & $T H$ \\ \hline$T T$ & $T T$ & $T T$ & $T H$ & $T H$ \\ \hline$H H$ & $H T$ & $H T$ & $H T$ & $T H$ \\ \hline$H H$ & $H H$ & $H H$ & $H H$ & $H H$ \\ \hline \end{tabular} The simulated probability of the event $T \mathrm{~T}$ is $\square$ (Type an integer or decimal rounded to two decimal places as needed.)

Solution

Solution Steps

To find the simulated probability of the event "TT" (both coins showing tails), we need to count the number of times "TT" appears in the given simulation results and then divide that by the total number of trials (25 in this case).

Step 1: Count the Occurrences of "T T"

From the simulation results, we have the following outcomes:

\[ \text{results} = \begin{bmatrix} T H & T T & T & H H & T \\ H H & H H & H H & H T & T H \\ T T & T T & T T & T H & T H \\ H H & H T & H T & H T & T H \\ H H & H H & H H & H H & H H \end{bmatrix} \]

We flatten this list to count the occurrences of the outcome $ T T $. The flattened results are:

\[ \text{flattened\_results} = [T H, T T, T, H H, T, H H, H H, H H, H T, T H, T T, T T, T T, T H, T H, H H, H T, H T, H T, T H, H H, H H, H H, H H, H H] \]

Counting the occurrences of $ T T $, we find:

\[ \text{count\_tt} = 4 \]

Step 2: Calculate the Total Trials

The total number of trials conducted in the simulation is:

\[ \text{total\_trials} = 25 \]

Step 3: Compute the Simulated Probability

The simulated probability $ P(T T) $ is calculated using the formula:

\[ P(T T) = \frac{\text{count\_tt}}{\text{total\_trials}} = \frac{4}{25} = 0.16 \]