Please write a detailed solution for each of the following problems and upload y

Question

Please write a detailed solution for each of the following problems and upload your work to Taskstream in a PDF format via eCourse. Note: Suppose a study is conducted using adults in a particular county. They found that 52% of the adults in the county are Computation Skills) males. In addition to the above, they found that 9.5% of males smoke cigars, whereas 1.7% of females smoke cigars. If an adult is chosen randomly, what is the probability that an adult is a male given that selected adult smokes cigars?

Explanation / Answer

Here we are given that P( males ) = 0.52, therefore P( females ) = 1 - 0.52 = 0.48

P( smoke | males ) = 0.095

P( smoke | females ) = 0.017

Using law of total probability, we get:

P( smoke ) = P( smoke | males )P( males ) + P( smoke | females )P( females )

P( smoke ) = 0.52*0.095 + 0.48*0.017 = 0.05756

Now using bayes theorem, the probability that the smoker is male is computed here as:

P( male | smoke ) = P( smoke | males )P( males ) / P( smoke )

P( male | smoke ) = 0.52*0.095 / 0.05756

P( male | smoke ) = 0.8582

Therefore 0.8582 is the required probability here.

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