The probability that an event A happens in one trial of an experiment is 0.7. Three independent rials of the experiment are performed. The probability that the event A happens at least once is

Options

A. `*657`
B. `*973`
C. `*027`
D. `*343`

Answer

To find the probability that event A happens at least once in three independent trials, we can follow these steps:

### Step 1: Identify the probability of event A happening in one trial
Given that the probability of event A happening in one trial is \( P(A) = 0.7 \).

### Step 2: Calculate the probability of event A not happening in one trial
The probability that event A does not happen in one trial is given by:
\[ P(A') = 1 - P(A) = 1 - 0.7 = 0.3 \]

### Step 3: Calculate the probability of event A not happening in all three trials
Since the trials are independent, the probability that event A does not happen in all three trials is:
\[ P(A' \text{ in all 3 trials}) = P(A')^3 = (0.3)^3 = 0.027 \]

### Step 4: Calculate the probability of event A happening at least once in three trials
The probability that event A happens at least once in three trials is the complement of the probability that it does not happen at all:
\[ P(A \text{ at least once}) = 1 - P(A' \text{ in all 3 trials}) = 1 - 0.027 = 0.973 \]

### Final Answer
The probability that event A happens at least once in three independent trials is:
\[ \boxed{0.973} \]