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(AB) 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(AB) = (eq4.4) P(BA) = Note 3: Based on the conditional probability, we can write PM and B) = P(A]B)*P(B)
or P(A and B) = P(BA) a P(A). Now, if P(AB) = P(A) and P(BA) = 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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 Spring '11
 ABEYSUNDARA
 Statistics

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