Answer
Marginal probability is the probability of a single event without consideration of any other event.
For example,
The table given shows the distribution of 100 workers based on two characteristics: gender (male or female) and hobby (reading or swimming).
One worker is selected at random from these 100 workers.
The marginal probablities are calculated as follows:
P(male) = $\frac{Number of male workers}{Total number of workers} = \frac{50}{100} = 0.5$
P(female) = $\frac{Number of female workers}{Total number of workers} = \frac{50}{100} = 0.5$
P(reading) = $\frac{40}{100} = 0.4$
P(swimming) = $\frac{60}{100} = 0.6$
Conditional probability is the probability that an event will occur given that another event has already occurred. If A and B are two events, then the conditional probability of A given B is written as: P(A|B).
For example:
According to the table,
P(reading|female) = $\frac{30}{50} = 0.6$
P(swimming|male) = $\frac{40}{50} = 0.8$
The probability P(reading|female) and P(swimming|male) are the conditional probability that a randomly selected worker is reading (or swimming) given that this worker is a female (or male).
Work Step by Step
See above
