Probability is the measure of likelihood that an event will occur. It ranges from 0 (impossible) to 1 (certain), expressed as a fraction, decimal, or
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What is the difference between probability and odds?
Probability is the ratio of favorable to total outcomes, ranging from 0 to 1. Odds express the ratio of favorable to unfavorable outcomes (e.g., 2:3 odds). A probability of 0.4 equals odds of 2:3.
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Can you multiply probabilities when events are not independent?
No, for independent events only. For dependent events, use conditional probability: P(A and B) = P(A) × P(B given A). Drawing two cards without replacement requires using conditional probability.
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Why is a 95% accurate test sometimes unreliable?
If a disease is very rare (e.g., 1 in 1000), even a 95% accurate test will have many false positives. Among 1000 people, 1 has the disease (99% chance of positive). 999 don't have it, but 5% test positive (50 false positives). So a positive test means only about 2% chance of actually having it (1 in 51).
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