A mini-computer system contains two components, A and B. The system will function so long
as either A or B functions. The probability that A functions is 0.95, the probability that B
functions is 0.90, and the probability that both function is 0.88. What is the probability that the
system functions?
Wouldn't that be the probability that both A and B function?
However, the probability of both events occurring is found by multiplying the probabilities of the individual events. I get .855.
To find the probability that the system functions, we can use the concept of complementary probability.
The complementary probability is the probability that an event does not happen. In this case, the complementary event is the system not functioning.
Let's calculate the probability that the system does not function:
1. The probability that A does not function is 1 - 0.95 = 0.05.
2. The probability that B does not function is 1 - 0.90 = 0.10.
3. The probability that both A and B do not function is the product of their individual probabilities: 0.05 * 0.10 = 0.005.
Now, since we have the probability that the system does not function, we can find the probability that it does function by subtracting this value from 1 (since the sum of the probabilities of an event and its complementary event is always 1):
Probability that the system functions = 1 - 0.005 = 0.995.
Therefore, the probability that the system functions is 0.995, or 99.5%.