The probability of happening of an event in a trial is 0.5. The probability of happening of the event atlest once if the experiment is repeated 3 times is

Options

A. 1.589
B. 0.567
C. 0.875
D. 1.9275

Answer

To solve the problem, we need to find the probability of an event happening at least once when the experiment is repeated three times, given that the probability of the event occurring in a single trial is 0.5.

### Step-by-Step Solution:

1. **Identify the probability of the event occurring in a single trial**:
- Given that the probability of the event occurring (P(E)) is 0.5.

2. **Calculate the probability of the event not occurring in a single trial**:
- The probability of the event not occurring (P(E')) is given by:
\[ P(E') = 1 - P(E) = 1 - 0.5 = 0.5 \]

3. **Determine the probability of the event not occurring in all three trials**:
- Since the trials are independent, the probability of the event not occurring in all three trials is:
\[ P(E' \text{ in 3 trials}) = P(E') \times P(E') \times P(E') = 0.5 \times 0.5 \times 0.5 = 0.125 \]

4. **Calculate the probability of the event occurring at least once in three trials**:
- The probability of the event occurring at least once is the complement of the event not occurring at all in three trials:
\[ P(\text{at least one occurrence in 3 trials}) = 1 - P(E' \text{ in 3 trials}) = 1 - 0.125 = 0.875 \]

5. **Final answer**:
- Therefore, the probability of the event occurring at least once when the experiment is repeated three times is:
\[ \boxed{0.875} \]