Conditional Probability
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probability marginal probability:PA:PABPAB = PA | BPB
Conditional probability is the probability of an event occurring given that another event has occurred. It is denoted by P(A|B), which means the probability of event A occurring given that event B has occurred.
The formula for conditional probability is:
P(A|B) = P(A and B) / P(B)
where P(A and B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.
For example, let's say we have a deck of cards and we want to find the probability of drawing a spade given that we have already drawn a black card. We can use conditional probability as follows:
P(Spade|Black) = P(Spade and Black) / P(Black)
The probability of drawing a spade and a black card is 13/52 (since there are 13 black spades in the deck), and the probability of drawing a black card is 26/52 (since half of the deck is black). Therefore,
P(Spade|Black) = (13/52) / (26/52) = 1/2
So the probability of drawing a spade given that we have already drawn a black card is 1/2.
The formula for conditional probability is:
P(A|B) = P(A and B) / P(B)
where P(A and B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.
For example, let's say we have a deck of cards and we want to find the probability of drawing a spade given that we have already drawn a black card. We can use conditional probability as follows:
P(Spade|Black) = P(Spade and Black) / P(Black)
The probability of drawing a spade and a black card is 13/52 (since there are 13 black spades in the deck), and the probability of drawing a black card is 26/52 (since half of the deck is black). Therefore,
P(Spade|Black) = (13/52) / (26/52) = 1/2
So the probability of drawing a spade given that we have already drawn a black card is 1/2.
CFA考试视频Conditional ProbabilityCFA一级视频
