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

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The discussion revolves around calculating the probability that a system with two components, A and B, will function. The individual probabilities are given as 0.95 for A and 0.90 for B, with a joint probability of 0.88 for both functioning. To find the overall probability that the system functions, the formula used is P(A or B) = P(A) + P(B) - P(A and B). Participants are encouraged to share their attempts and specific challenges to receive targeted assistance. The conversation emphasizes collaborative problem-solving in probability theory.
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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.
 
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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:
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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