Answered

9-2: Probability Distributions and Frequency Tables

A student conducts a probability experiment by tossing 3 coins one after the other. Using the results below, what is the experimental probability that exactly two tails will occur in the next three tosses?

\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline Coin Toss Result & HHH & HHT & HTT & HTH & THH & THT & TTT & TTH \\
\hline Frequency & 5 & 7 & 9 & 6 & 2 & 9 & 10 & 2 \\
\hline
\end{tabular}

A. [tex]$13 / 50$[/tex]
B. [tex]$17 / 50$[/tex]
C. [tex]$4 / 50$[/tex]
D. [tex]$2 / 5$[/tex]



Answer :

To determine the experimental probability that exactly two tails will occur in the next three tosses based on the given frequency table, follow these steps:

1. Identify the relevant outcomes:
- The outcomes where exactly two tails occur in three tosses are HTT, THT, and TTH.

2. Find the frequencies of these specific outcomes:
- From the table, the frequency of HTT is 9.
- The frequency of THT is 9.
- The frequency of TTH is 2.

3. Sum the frequencies of the relevant outcomes:
- Add the frequencies of HTT, THT, and TTH:
[tex]\[ 9 + 9 + 2 = 20 \][/tex]

4. Calculate the total number of tosses:
- Sum all the frequencies in the table:
[tex]\[ 5 + 7 + 9 + 6 + 2 + 9 + 10 + 2 = 50 \][/tex]

5. Determine the experimental probability:
- The experimental probability is the frequency of obtaining exactly two tails divided by the total number of tosses:
[tex]\[ \frac{20}{50} = \frac{2}{5} \][/tex]

Thus, the experimental probability that exactly two tails will occur in the next three tosses is [tex]\( \frac{2}{5} \)[/tex].

The correct answer is:
[tex]\[ \text{D. } \frac{2}{5} \][/tex]