108k views
3 votes
A machine has three components A, B and C. The probability of A working is 7/10. If A is working, the probability of B working is 1/3 . If A is not working, then the probability of B working is 1/3. If A and B are working, the probability of C working is 5/6, otherwise it is 1/10 . The machine only works if C is working

2 Answers

12 votes

Final answer:

The question involves finding the probability of a machine working based on the probability of its components working. Using the rules of probability, we calculate the likelihood of components A, B, and C functioning, to ultimately determine the probability of the machine working, which depends solely on component C.

Step-by-step explanation:

The problem given discusses the functionality of a machine based on its components A, B, and C. The machine works only if component C is working. We start by finding the probability of each component working, and then use those probabilities to find the likelihood of the machine working as a whole. We apply basic rules of probability such as the multiplication rule (P(A AND B) = P(A|B)P(B)), and conditional probability (P(A|B) is the probability of A given B has occurred).

The probability of component A working is given as 7/10. This is our starting point. Next, regardless of whether A is working or not, the probability of B working is 1/3. The tricky part comes with component C: if both A and B are working, the probability of C working is 5/6; otherwise, it is just 1/10. To compute the probability of the entire machine working, we must consider the probability of A and B both working, which then influences the probability of C.

Let's go through the steps:

  1. Calculate the probability of A and B both working:
    P(A and B) = P(B|A)P(A) = (1/3)(7/10) = 7/30.
  2. Calculate the probability of C working given A and B are both working, and then find the overall probability of C working based on A and B's status. This involves considering the two scenarios: A and B are both working or at least one of them is not working.
  3. Finally, since the machine works only if component C is working, the probability of the machine working is the same as the probability of C working in the 'best-case' scenario (A and B both working).

Once we have calculated the probabilities of these events, we can know the likelihood of the machine being operational.

User Edvard Rejthar
by
8.6k points
4 votes

Answer:

false

Step-by-step explanation:

what is the question

User Razzildinho
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories