To determine the probability that two independent events will both occur, we need to follow these steps:
1. Identify the probability of each individual event:
- According to the problem, each event has an equal likelihood of occurring, which is 50%.
- In probability terms, this is expressed as 0.5 (since probabilities range from 0 to 1).
2. Understand the concept of independent events:
- When two events are independent, the occurrence of one event does not affect the occurrence of the other.
- This means the probability of both events happening together is the product of their individual probabilities.
3. Calculate the combined probability:
- Let's denote the events as [tex]\(A\)[/tex] and [tex]\(B\)[/tex].
- The probability of event [tex]\(A\)[/tex] occurring is [tex]\(P(A) = 0.5\)[/tex].
- The probability of event [tex]\(B\)[/tex] occurring is [tex]\(P(B) = 0.5\)[/tex].
- For independent events, the combined probability of both events occurring [tex]\(P(A \text{ and } B)\)[/tex] is:
[tex]\[
P(A \text{ and } B) = P(A) \times P(B)
\][/tex]
- Substituting the given probabilities:
[tex]\[
P(A \text{ and } B) = 0.5 \times 0.5 = 0.25
\][/tex]
4. Convert the probability to a percentage:
- To express this probability as a percentage, multiply by 100:
[tex]\[
0.25 \times 100 = 25\%
\][/tex]
Therefore, the probability that both independent events with a 50% chance each will occur is [tex]\( 25\% \)[/tex].
The correct answer is:
[tex]\[ \boxed{25\%} \][/tex]
