Sandert Computer Company manufactures memory chips in lots of ten chips. From past experience, Sandert knows that 70% of

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Sandert Computer Company manufactures memory chips in lots of
ten chips. From past experience, Sandert knows that 70% of all lots
contain 10% (1 out of 10) defective chips, they call these type of
batches a “good batch”, and 30% of all lots contain 50% (5 out of
10) defective chips, these lots are called “bad batches”. If a good
batch of chips is sent on to the next stage of production,
processing costs of $1,000 are incurred, and if a bad batch is sent
on to the next stage of production, processing costs of $4,000 are
incurred. Sandert also has the alternative of reworking a batch at
a cost of $1,000. A reworked batch is sure to be a good batch.
Alternatively, for a cost of $100, Sandert can test one chip from
each batch in an attempt to determine whether the batch is bad or
not.
a) Identify the states of nature for this problem.
b) Identify the experiment, state the possible outcomes from it
and find the posterior probabilities.
c) Draw and analyze the decision tree for this problem and state
the optimal policy incluiding the optimal expected payoff.