Probability of happening of an event in an experiment is 0.4 . The probability of happening of the event atleast once , if the experiment is repeated 3 times under similar condition is

Options

A. `(1)/(16)`
B. `(13)/(16)`
C. `(98)/(125)`
D. `(1)/(4)`

Answer

To solve the problem, we need to find the probability of an event occurring at least once when the experiment is repeated three times, given that the probability of the event occurring in a single experiment is 0.4.

### Step-by-Step Solution:

1. **Identify the Probability of the Event**:
- Let \( P \) be the probability of the event occurring in a single trial.
- Given \( P = 0.4 \).

2. **Calculate the Probability of the Event Not Occurring**:
- The probability of the event not occurring, denoted as \( Q \), is calculated as:
\[ Q = 1 - P = 1 - 0.4 = 0.6 \]

3. **Determine the Number of Trials**:
- The experiment is repeated \( n = 3 \) times.

4. **Calculate the Probability of the Event Occurring at Least Once**:
- The probability of the event occurring at least once can be calculated using the complement rule:
\[ P(\text{at least one occurrence}) = 1 - P(\text{no occurrences}) \]
- The probability of the event not occurring in all three trials is:
\[ P(\text{no occurrences}) = Q^n = 0.6^3 \]
- Calculate \( 0.6^3 \):
\[ 0.6^3 = 0.216 \]

5. **Final Calculation**:
- Now, substitute this back into the complement formula:
\[ P(\text{at least one occurrence}) = 1 - P(\text{no occurrences}) = 1 - 0.216 = 0.784 \]

6. **Convert to Fraction**:
- To express this probability as a fraction, we can write:
\[ 0.784 = \frac{784}{1000} \]
- Simplifying this fraction:
\[ \frac{784 \div 8}{1000 \div 8} = \frac{98}{125} \]

### Conclusion:
The probability of the event occurring at least once when the experiment is repeated three times is:
\[ \frac{98}{125} \]