If the average time between failure for a battery is 36 months, what is the probability of failure within 36 months and what is the probability that a system which is composed of two such batteries fails within 36 months if both must work for the system to work.
The avearge time between failures for a watch battery is 36 months. This means that if n batteries are tested and the time required for them to fail recorded, the average of all the values is 36 months. Half the batteries fail before 36 months and the other half fail after 36 months. Here, the individual values can vary wildly, for example if one battery fails after a month and another battery fails after 71 months we still get an average of 36 months.
The probability of failure of a battery within 36 months is 1/2 or 50%.
As the system has two batteries and each of them needs to work for the system to work, the probability that the system fails within 36 months is 1 - (1/2)*(1/2) = 0.75 or 75%.
The probability of failure within 36 months is 50%. The probability that a system with two batteries fails within 36 months is 75%.