5 Questions
What does conditional probability P(B|A) represent?
The probability of event B occurring after event A has occurred
According to the multiplication theorem of probability, what is the probability of the intersection of two events with probabilities greater than 0?
Equal to the product of their individual probabilities
In a city where overlapping readerships exist, what is the probability of reading at least one newspaper if 20% read A, 16% read B, and 14% read C?
Between 20% and 35%
In selecting a ticket numbered from 1 to 30, what is the probability of selecting a ticket that is neither a multiple of five nor three?
$4/15$
If events A and B are independent, what is the probability of both events happening?
$P(A) \times P(B)$
Study Notes
- Conditional probability is defined as the probability of event B occurring after event A has occurred, denoted as P(B|A), calculated as the probability of the intersection of B and A divided by the probability of A.
- The multiplication theorem of probability states that if events A and B have probabilities greater than 0, the probability of their intersection is equal to the product of their individual probabilities.
- When calculating the probability of reading at least one newspaper in a city where 20% read A, 16% read B, and 14% read C, along with overlapping readerships, the percentage is found to be 35%.
- In another scenario where one ticket is randomly selected from tickets numbered 1 to 30, the probability of selecting a ticket that is a multiple of five or three is calculated to be 1/3 and 7/15 respectively.
Test your knowledge of conditional probability, the multiplication theorem, and calculating probabilities of overlapping events. Explore scenarios involving selecting tickets and reading newspapers to assess your grasp of fundamental probability concepts.
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