8D - Conditional probability
8D - Content video: Conditional probability
This video covers the theory and several examples relating to conditional probability.
■ Meet Mr and Mrs Smith… For this example, we will assume that the probability of a couple having a boy or a girl is equal; that is, \(Pr(B)=0.5\) and \(Pr(G)=0.5\). Mr and Mrs Smith have two children, at least one of which is a girl. What is the probability that both of their children are girls? (Answer in the video)
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Often we are interested in the probability of \(A\) occurring, given that event \(B\) has already occurred. This is conditional probability. Mathematically, we denote conditional probability as \(Pr(A|B)\). We read this a “the probability of \(A\) occurring given \(B\) has occurred”. \[Pr(A|B)=\frac{Pr(A \cap B)}{Pr(B)}\] where \(Pr(B) \neq 0\).
The conditional probability formula can be rearranged to give the multiplication rule of probability: \[Pr(A|B) \times Pr(B)=Pr(A \cap B)\] This formula is used when multiplying probabilities along the branches of tree diagram.
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Videos exploring probability
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