The theoretical probability of an event is a measure of the likelihood that event will occur, calculated based on the possible outcomes. In the case of tossing a fair coin, there are two possible outcomes for each toss: heads (H) and tails (T).
When tossing a coin twice, we can list out all the possible outcomes for the two tosses. The outcomes can be represented as follows:
- HH (two heads)
- HT (first toss heads, second toss tails)
- TH (first toss tails, second toss heads)
- TT (two tails)
This results in a total of 4 possible outcomes: HH, HT, TH, and TT.
Out of these 4 outcomes, only 1 outcome results in two heads (HH).
To calculate the theoretical probability of getting two heads when tossing a coin twice, we use the formula for probability:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
In this scenario, the number of favorable outcomes (getting two heads) is 1, and the total number of possible outcomes is 4. Therefore, the probability can be calculated as follows:
Probability = 1 / 4
This simplifies to:
Probability = 0.25
Or in percentage terms:
Probability = 25%
Thus, the theoretical probability of obtaining two heads when tossing a coin twice is 25%.