Question
The experiment tossing three coins simultaneously. The experiment was carried out 100 times, and it was noted that three heads and its theoretical probability? Write the answer in the simplest form of fraction. (1 point)
Answers
GPT-4o mini
To find the theoretical probability of obtaining three heads when tossing three coins, we first need to identify the total number of possible outcomes and the number of favorable outcomes.
When tossing three coins, each coin has 2 possible outcomes: heads (H) or tails (T). Therefore, the total number of outcomes when tossing three coins is given by:
\[
2^3 = 8
\]
The possible outcomes are: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.
Out of these 8 outcomes, only 1 outcome represents getting three heads (HHH).
Now, the probability \( P \) of getting three heads can be calculated using the formula for probability:
\[
P(\text{three heads}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{8}
\]
Thus, the theoretical probability of obtaining three heads when tossing three coins is:
\[
\frac{1}{8}
\]
This fraction is already in its simplest form.
When tossing three coins, each coin has 2 possible outcomes: heads (H) or tails (T). Therefore, the total number of outcomes when tossing three coins is given by:
\[
2^3 = 8
\]
The possible outcomes are: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.
Out of these 8 outcomes, only 1 outcome represents getting three heads (HHH).
Now, the probability \( P \) of getting three heads can be calculated using the formula for probability:
\[
P(\text{three heads}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{8}
\]
Thus, the theoretical probability of obtaining three heads when tossing three coins is:
\[
\frac{1}{8}
\]
This fraction is already in its simplest form.