Answer:
No, a reliability rating of 97% does not mean that out of the 100 times you use the device, there are 97 chances that the device will not fail.
Reliability is a measure of the probability that a device will perform its intended function without failure over a specified period of time or number of uses. In this case, a reliability rating of 97% means that the device is expected to function properly and not fail in 97 out of 100 uses or instances, on average.
So, in the context of your mountain climbing activity, it means that out of the estimated 100 times you use the safety hooks over the course of a year, you can expect the device to function correctly and not fail in approximately 97 instances. However, there is still a small possibility of failure in the remaining 3 instances, as no device can provide a guarantee of absolute reliability.