To determine the probability of obtaining no heads (i.e., both coin flips result in tails), we need to follow these steps:
1. Identify the Total Number of Flips:
The experiment involves flipping a coin twice 200 times. Each outcome is recorded with its frequency:
- Heads + Heads: 75 times
- Heads + Tails: 40 times
- Tails + Tails: 35 times
- Tails + Heads: 50 times
2. Calculate the Total Number of Flips:
Sum all the occurrences:
[tex]\[
\text{Total Flips} = 75 + 40 + 35 + 50 = 200
\][/tex]
3. Identify the Number of Outcomes with No Heads:
The only outcome where there are no heads is when both flips result in tails:
[tex]\[
\text{No Heads Outcomes} = 35
\][/tex]
4. Calculate the Probability of No Heads:
The probability of getting no heads is the number of no heads outcomes divided by the total number of flips, multiplied by 100 to convert it to a percentage:
[tex]\[
P(\text{No Heads}) = \left(\frac{\text{No Heads Outcomes}}{\text{Total Flips}}\right) \times 100 = \left(\frac{35}{200}\right) \times 100 = 17.5\%
\][/tex]
Thus, the probability of getting no heads is [tex]\(17.5\%\)[/tex]. Therefore, the correct answer is [tex]\(17.5\%\)[/tex].
