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A market research firm polled owners of new Tesla automobiles. They found that 20% of the...

A market research firm polled owners of new Tesla automobiles. They found that 20% of the owners experienced a problem in the first month of ownership. They also found that 90% of those who did not experience a problem in the first month were satisfied with their purchase but only 60% of those who did experience a problem in the first month were satisfied with their purchase. Let E be the event “experienced a problem in the first month of ownership” and let S be the event “satisfied with their purchase”. Are the events E and S independent? Why or why not?

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Answer #1

We are given :

P(E) = 0.20

Let denote the event “did not experienced a problem in the first month of ownership”

P() = 1 - 0.20 = 0.80

Now,

P(S | ) = 0.90

Also,

P( S | E ) = 0.60

We have :

E and S will be independent if :

We have,

hence,

Therefore,

Events E and S are not independent

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