p(a,b) = the probability that event a and b happen at the same time. p(a|b) = the probability that event a happens due to the event b happens. For me, I think the meaning is quite the same.
P(A given B) is the chances that A will occur, given B already happened.
Example of P(A and B): What are the chances of getting double sixes when rolling a pair of dice? The roll of the first die is event A and the roll of the second die is event B. The chances are 1/36 because each die has a 1 in 6 chance of getting a six, and the outcomes are independent, so the chances are just 1/6 multiplied by 1/6.
Example of P(A given B): What is the chances of getting double sixes, given that the first die has already stopped rolling and is a 6 (event A is 6). The answer is 1/6, because the chance of the second die stopping on 6 (event B) is 1/6, and we already know A is a six.
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Answer:
p(a,b) = the probability that event a and b happen at the same time. p(a|b) = the probability that event a happens due to the event b happens. For me, I think the meaning is quite the same.
Answer:
P(A and B) is the chances both A and B will occur
P(A given B) is the chances that A will occur, given B already happened.
Example of P(A and B): What are the chances of getting double sixes when rolling a pair of dice? The roll of the first die is event A and the roll of the second die is event B. The chances are 1/36 because each die has a 1 in 6 chance of getting a six, and the outcomes are independent, so the chances are just 1/6 multiplied by 1/6.
Example of P(A given B): What is the chances of getting double sixes, given that the first die has already stopped rolling and is a 6 (event A is 6). The answer is 1/6, because the chance of the second die stopping on 6 (event B) is 1/6, and we already know A is a six.
Step-by-step explanation: