Answered

IDNLearn.com provides a collaborative environment for finding and sharing answers. Get prompt and accurate answers to your questions from our community of knowledgeable experts.

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 appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.