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]
