What is the probability that a system will function with two components A and B?

Click For Summary
SUMMARY

The probability that a system with two components, A and B, will function is calculated using the formula for the union of two events. Given that the probability of A functioning is 0.95, the probability of B functioning is 0.90, and the probability of both A and B functioning is 0.88, the probability that the system functions is determined to be 0.97. This is derived from the equation P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

PREREQUISITES
  • Understanding of basic probability concepts
  • Familiarity with probability notation and formulas
  • Knowledge of union and intersection of events
  • Ability to perform basic arithmetic operations with decimals
NEXT STEPS
  • Study the principles of probability theory
  • Learn about conditional probability and independence of events
  • Explore applications of probability in system reliability analysis
  • Investigate more complex probability scenarios involving multiple components
USEFUL FOR

Students in statistics, engineers working on system reliability, and anyone interested in understanding the functionality of systems with multiple components.

ericndegwa
Messages
2
Reaction score
0
Need help


A system contains two components A & B. The system will function so long as either A or B functions. The probability that A functions is 0.95, the probability that B functions is 0.90, & the probability both function is 0.88. What is the probability that the system functions.
 
Physics news on Phys.org
hi ericndegwa! welcome to pf! :wink:

show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 

Similar threads

Undergrad Sample space, outcome, event, random variable, probability...
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Conditional and joint probabilities of statistically dependent events
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad On the expected value of a sum of a random number of r.v.s.
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Probability Density Function of the Product of Independent Variables
  • · Replies 3 ·
Replies
3
Views
2K
MHB What Is the Probability of Distributing Remaining Trump Cards in Bridge?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Calculation of average damage using analytical methods
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad What is the probability that the product of the digits is odd?
  • · Replies 13 ·
Replies
13
Views
3K
Graduate Concrete examples of randomness in math vs. probability theory
  • · Replies 11 ·
Replies
11
Views
3K
High School Relative And Absolute Probability (Probability Of Picking A Red Ball)
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Conditional probabilities of conditioned probabilities
  • · Replies 4 ·
Replies
4
Views
2K