It is estimated that 1.3% of the matches produced at a factory are damaged in some way. A household box contains 462 matches.
a. Calculate the expected number of damaged matches in a household box.
b. Find the variance of the number of damaged matches and the variance of the number of undamaged matches in a household box.
c. Show that approximately 10.4% of the household boxes are expected to contain exactly eight damaged matches.
d. Calculate the probability that at least one from a sample of two household boxes contains exactly eight damaged matches.
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