The probability of happening an event A in one trial is 0.4. Find the probability that the event A happens at least one in three independent trials

To solve this problem, it's easier to find the probability of the opposite event (the event A does not happen in any of the three trials) and then subtract it from 1.

Step 1: Find the probability of event A not happening in a single trial. Since the probability of event A happening is 0.4, the probability of it not happening is 1 - 0.4 = 0.6.

Step 2: Find the probability of event A not happening in three independent trials. Since the trials are independent, the probabilities multiply. So, the probability of event A not happening in three trials is 0.6 * 0.6 * 0.6 = 0.216.

Step 3: Find the probability of event A happening at least once in three trials. This is the opposite of the event A not happening in any of the trials. So, subtract the probability found in step 2 from 1. The probability of event A happening at least once is 1 - 0.216 = 0.784.

So, the probability that the event A happens at least once in three independent trials is 0.784.