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I am having hard time figuring out if it is a conditional probability or an "and" probability under the following types of problems.

When a student is absent, the probability of the student being sick is .6

In such a sentence, I am not quite sure if the probability is conditional or the probability when the student is sick and absent.

Which one would it be?

As a matter of fact, is there a rule of thumb to be able to tell if it is conditional or not?

I feel as though every time I deal with these kind of problems I get stuck.

hyg17
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    This definitely sounds like a conditional probability. When a student is absent, then its probability of being sick is 0.6 – Marc Apr 14 '14 at 18:03
  • "When", "If", "Given that", "Given that you know that", "If you know that" all imply conditional. They all suggest a "...then such and such..." should be in the sentence i.e. an implication. The "and" is much more straightforward - it should pretty much say "and" without the truth of one part of the sentence implying the truth of the other.. – Paul Apr 14 '14 at 18:54
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    So, if someone said "the probability that a student is absent and sick is .6" would be an and probability. – hyg17 Apr 15 '14 at 02:24

2 Answers2

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Now, given that the student is absent, the probability of a student being sick is 0.6.

The student being absent is treated as an event that has happened, so we are conditioning on that

Nikolas
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AlistairLR112
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When a student is absent, the probability of the student being sick is .6

In such a sentence, I am not quite sure if the probability is conditional or the probability when the student is sick and absent.

The rule of thumb is that when provided a probability for an event occurring under some condition, you are being presented a conditional probability.

Here, "when a student is absent" is a condition, under which the probability for the event "student being sick" is being measured.

Community
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Graham Kemp
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