Answered

Find solutions to your problems with the help of IDNLearn.com's knowledgeable users. Ask your questions and receive detailed and reliable answers from our experienced and knowledgeable community members.

An aircraft has two independent computer systems, both performing the same critical task. Each system has a probability of failing on a flight as follows: 0.3 for System 1 and 0.03 for System 2.

What is the probability that both systems will fail on a flight?

[tex]\square[/tex]

Sagot :

GinnyAnsweridn
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.
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.