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

In summary, conditional probability is a mathematical concept that measures the likelihood of an event occurring given that another event has already occurred. It is calculated by dividing the probability of the joint occurrence of two events by the probability of the occurrence of the first event. The difference between conditional probability and unconditional probability is that the former takes into account additional information or conditions. Conditional probability has many real-life applications and cannot be greater than 1.
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ericndegwa
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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:
 

What is conditional probability?

Conditional probability is a mathematical concept that measures the likelihood of an event occurring given that another event has already occurred. It takes into account the relationship between two events and helps us understand how the probability of one event changes when we have information about the other event.

How is conditional probability calculated?

Conditional probability is calculated by dividing the probability of the joint occurrence of two events by the probability of the occurrence of the first event. In other words, it is the probability of event A given that event B has occurred, which is denoted as P(A|B) and is equal to P(A and B) / P(B).

What is the difference between conditional probability and unconditional probability?

Conditional probability takes into account additional information or conditions, while unconditional probability does not. Unconditional probability is calculated by simply dividing the number of desired outcomes by the total number of possible outcomes, whereas conditional probability takes into account the relationship between two events.

What is the importance of conditional probability in real life?

Conditional probability has many real-life applications, such as in predicting the likelihood of a disease given a positive test result, or the probability of a car accident given the driver's age and gender. It is also used in decision-making processes, risk analysis, and machine learning algorithms.

Can conditional probability be greater than 1?

No, conditional probability cannot be greater than 1. This is because the probability of two events occurring together (the joint probability) can never be greater than the probability of either event occurring alone. Therefore, the conditional probability, which is the joint probability divided by the probability of the first event, will always be less than or equal to 1.

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