Question

In Problem $3.66 \mathrm{a},$ find the conditional probability that relays 1 and 2 are both closed given that a current flows from $A$ to $B$

Name: Problem 68, Chapter 3: A First Course in Probability
Uploaded: 2022-03-17T10:47:22-08:00
Duration: 4 min 16 s
Channel: Hunza Gilgit
Description: In Problem 3.66 a, find the conditional probability that relays 1 and 2 are both closed given that a current flows from A to B

   In Problem $3.66 \mathrm{a},$ find the conditional probability that relays 1 and 2 are both closed given that a current flows from $A$ to $B$

A First Course in Probability

Sheldon Ross 9th Edition

Chapter 3, Problem 68

Instant Answer

Solved by Expert Hunza Gilgit

03/17/2022

Step 1

Let $ C $ be the event that a current flows from $ A $ to $ B $. Let $ R_1 $ be the event that relay 1 is closed, and $ R_2 $ be the event that relay 2 is closed. We are interested in finding $ P(R_1 \cap R_2 \mid C) $, the probability that both relays Show more…

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In Problem $3.66 \mathrm{a},$ find the conditional probability that relays 1 and 2 are both closed given that a current flows from $A$ to $B$

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Key Concepts

Conditional Probability

This concept involves calculating the likelihood of an event occurring given that another event has already occurred. The formal definition is P(A|B) = P(A and B) / P(B), which is central to solving problems where outcomes are interdependent.

System Reliability

System reliability is concerned with determining the probability that a system or network composed of multiple components functions as intended. This analysis typically looks at how individual component states, such as a relay being 'closed' or 'open', combine to yield the overall operation of the system.

Network Connectivity

Network connectivity refers to the analysis of whether a system, such as an electrical circuit or network, is connected in a manner that allows current to flow from a source point to a destination point. It requires understanding the arrangement and operational status of various components to determine the existence of a conducting path.

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