To determine the probability that both independent computer systems on an aircraft will fail on a flight, we can use the concept of independent events in probability theory.
Given information:
- Probability of failure for System 1 ([tex]\( P(F_1) \)[/tex]) = 0.3
- Probability of failure for System 2 ([tex]\( P(F_2) \)[/tex]) = 0.03
Since the systems are independent, the probability that both systems will fail simultaneously is the product of their individual probabilities of failure.
Step-by-step solution:
1. Identify the probability of failure for System 1 ([tex]\( P(F_1) \)[/tex]).
2. Identify the probability of failure for System 2 ([tex]\( P(F_2) \)[/tex]).
3. Multiply these probabilities to obtain the probability that both systems will fail.
Mathematically, this is represented as:
[tex]\[ P(F_1 \; \text{and} \; F_2) = P(F_1) \times P(F_2) \][/tex]
Plugging in the given values:
[tex]\[ P(F_1 \; \text{and} \; F_2) = 0.3 \times 0.03 \][/tex]
[tex]\[ P(F_1 \; \text{and} \; F_2) = 0.009 \][/tex]
Therefore, the probability that both computer systems will fail on a flight is 0.009.
