Question

An experiment is conducted with a coin. The results of the coin being flipped twice 200 times is shown in the table.


Outcome Frequency
Heads, Heads 40
Heads, Tails 75
Tails, Tails 50
Tails, Heads 35


What is the P(No Heads)?
85%
75%
50%
25%

Answer 1

To find the probability of no heads (P(No Heads)) from the results of the coin flips, we first identify the outcomes that correspond to having no heads:

- Tails, Tails (TT)
- Tails, Heads (TH)

The frequencies for these outcomes are:
- Tails, Tails: 50
- Tails, Heads: 35

Now we will calculate the total frequency of these outcomes:

- Total frequency of no heads = Frequency of Tails, Tails + Frequency of Tails, Heads
- Total frequency of no heads = 50 + 35 = 85

Next, we calculate the total number of experiments:

- Total experiments = 200

Now, we can calculate the probability of no heads:

\[
P(\text{No Heads}) = \frac{\text{Total frequency of no heads}}{\text{Total experiments}} = \frac{85}{200} = 0.425
\]

To convert this to a percentage:

\[
P(\text{No Heads}) \times 100 = 42.5\%
\]

Since this value is not listed among the options given (85%, 75%, 50%, 25%), it appears there might be confusion in the interpretation of "no heads".

The only outcome representing no heads is "Tails, Tails" (TT), where we have:

\[
P(\text{No Heads}) = \frac{50}{200} = 0.25 \text{ (which is 25\%)}
\]

Thus, the answer is **25%**.