# 1. Consider the situation where bit strings of length four are randomly generated. Demonstrate…

1. Consider the situation where bit strings of
length four are randomly generated. Demonstrate whether or not the event of
production of bit strings containing an even number of 1s is independent of the
event of producing bit strings that end in a 1.

2. Show that the statement p(A,B|C) = p(A|C)
p(B|C) is
equivalent to both p(A|B,C) = p(A|C) and p(B|A,C)
= p(B|C).

3. In manufacturing a product, 85% of the products
that are produced are not defective. Of the products inspected, 10% of the good
ones are seen as defective and not shipped whereas only 5% of the defective
products are approved

1. Consider the situation where bit strings of
length four are randomly generated. Demonstrate whether or not the event of
production of bit strings containing an even number of 1s is independent of the
event of producing bit strings that end in a 1.

2. Show that the statement p(A,B|C) = p(A|C)
p(B|C) is
equivalent to both p(A|B,C) = p(A|C) and p(B|A,C)
= p(B|C).

3. In manufacturing a product, 85% of the products
that are produced are not defective. Of the products inspected, 10% of the good
ones are seen as defective and not shipped whereas only 5% of the defective
products are approved and shipped. If a product is shipped, what is the probability
that it is defective?

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