In the follow-up survey of the 300 households that actually purchased big screen TV, households were asked if they were satisfied with their purchase.Following table cross classifies the responses to the satisfaction question with their responses to whether the TV was an HDTV.Satisfied with Purchase?Type of TVYesNoTotalHDTV641680Not HDTV17644220Total24060300i.Determine whether being satisfied with the purchase and type of TV purchased are statistically independent.ii.Consider 80 households that purchased an HDTV. Here 64 households were satisfied with their purchases and 16 households are dissatisfied. Suppose 2 households are randomly selected from the set of 80 customers. Find the probability that both households are satisfied with their purchase.iii.What if the first household is returned to the sample after the satisfaction level is determined. Find the probability that both of the households sampled will be satisfied with their purchase.CASE STUDY 1 (CONTINUATION)

SOLUTION TO CASE STUDY 1 (CONTINUATION)

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The law of total probability allows us at times to evaluate probabilities of
events
–
that are difficult to obtain
–
but become easy to calculate once we condition on the occurrence of a related
event.
•
First we assume that the related event occurs and then we assume it does not
occur.
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Resulting conditional probabilities help us compute the total probability of
occurrence of the event of interest.
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Let us consider two events A & B
_
•
Law of total probability
:
P(A) = P(A
∩
B) + P(A
∩
B)
•
Using conditional probability
P(A) = P(A/B) P(B) + P(A/B) P(B)
(1)
LAW OF TOTAL PROBABILITY AND BAYES’ THEOREM
AUB
AUB
S

If A
1
,A
2
,………..,A
n
be a given set of n pair-wise mutually exclusive
events, one of which certainly occurs i.e.