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2011-10-02 22-18-59 11

2011-10-02 22-18-59 11 - (E Conditional Probability The...

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Unformatted text preview: (E) Conditional Probability: The probability of the occurrence of an event A, given the occurrence of another event B, denoted by P(A|B) is given by P(A and B) 13(3) ' Similarly, the conditional probability of event B given that event A has occurred as PM and B) PM) ' P(A|B) = (eq4.4) P(B|A) = Note 3: Based on the conditional probability, we can write PM and B) = P(A]B)*P(B) or P(A and B) = P(B|A) a P(A). Now, if P(A|B) = P(A) and P(B|A) = P(B), then A and B are said to be independent. (F) Independent Events: Two events A and B are said to be statistically independent if and only if P(A and B) = P(A) :- P(B). (eq4.7) EX 2 Suppose that an employment agency has found that 40% of the applicants are college grads and 30% of the applicants have had computer skills. The two characteristics are independent. Find the probability that the applicants are college grads and have had computer skills. 2. Application: computing Probability from a contingency table. EX 3 The manager of a shirt manufacture wants to study the connection between shifts and shirt quality. 600 shirts are randomly selected. The results are shown below: Shim Shim Em— Emmi—mm -_nnm _mmmm —.__.._._..___..-,___.__._.___._____ ...
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