To solve this problem, we need to determine the probability of getting "No Tails" when a coin is flipped twice, based on the given experimental data.
1. Understand the Events:
- "No Tails" means both coin flips must result in Heads. So, we are looking for the outcome (Heads, Heads).
2. Identify the Frequency of the Desired Event:
- From the table, the frequency of the outcome (Heads, Heads) is 40.
3. Calculate the Total Number of Trials:
- Total outcomes are calculated by summing up all the frequencies given.
- Total outcomes [tex]\( = 40 \text{ (Heads, Heads)} + 75 \text{ (Heads, Tails)} + 50 \text{ (Tails, Tails)} + 35 \text{ (Tails, Heads)} \)[/tex].
- Total outcomes [tex]\( = 40 + 75 + 50 + 35 \)[/tex].
- Total outcomes [tex]\( = 200 \)[/tex].
4. Compute the Probability of the Desired Event:
- Probability [tex]\( P(\text{No Tails}) \)[/tex] is the number of favorable outcomes (Heads, Heads) divided by the total number of trials.
- [tex]\( P(\text{No Tails}) = \frac{\text{Frequency of (Heads, Heads)}}{\text{Total Outcomes}} \)[/tex].
- [tex]\( P(\text{No Tails}) = \frac{40}{200} \)[/tex].
5. Convert the Probability to a Percentage:
- To convert the fraction to a percentage, we multiply by 100.
- [tex]\( P(\text{No Tails}) \times 100 = \frac{40}{200} \times 100 \)[/tex].
- [tex]\( P(\text{No Tails}) \times 100 = 20 \% \)[/tex].
Hence, the probability [tex]\( P \)[/tex] (No Tails) is [tex]\( 20 \% \)[/tex].
