Step 1 :First, we need to calculate the probability of a single pacemaker not malfunctioning due to firmware. This is equal to the number of non-faulty pacemakers divided by the total number of pacemakers. In this case, there are 5973 non-faulty pacemakers out of a total of 6245 pacemakers. So, the probability of a single pacemaker not malfunctioning is \(\frac{5973}{6245} = 0.956\).
Step 2 :Next, since the pacemakers are tested independently, the probability that all three pacemakers tested do not malfunction is the cube of the probability that a single pacemaker does not malfunction. So, the probability that all three pacemakers do not malfunction is \((0.956)^3 = 0.875\).
Step 3 :Final Answer: The probability that the firmware in the entire batch will be accepted is \(\boxed{0.875}\). This procedure is likely to result in the entire batch being accepted.