4. A total of 236 students took a survey that asked their gender and where they

Question

4. A total of 236 students took a survey that asked their gender and where they prefer to sit in class (front, middle, or back). The results are shown in the table below. Gender versus Seat Preference Seat Preference Middle 37 91 22 46 Total 150 86 236 Front Back Female Male Total 25 47 15 52 137 Suppose that one person in the sample is randomly selected. Write each answer as a decimal rounded to 3 places. a) Find P (prefers to sit in the middle). 2 pts) (2 pts b) Find P (prefers to sit in the middle and is male). (3 p c) Find P (prefers to sit in the middle or is male). d) Find P (prefers to sit in the middle | is male).

Explanation / Answer

a) The required probability here is computed as:

P( middle ) = n(middle ) / 236 = 137 / 236 = 0.5805

Therefore 0.5805 is the required probability here.

b) The required probability here is computed as:

P( middle and male ) = n(middle and male ) / 236 = 46 / 236 = 0.1949

Therefore 0.1949 is the required probability here.

c) The required probability here is computed as:

P( middle or male ) = [ n(middle ) + n(male and not middle ) ] / 236 = (137 + 15 + 25) / 236 = 0.75

Therefore 0.75 is the required probability here.

d) Using bayes theorem, we get here:

P( middle | male ) = P( middle and male ) / P( male ) = n(middle and male ) / n(male ) = 46 / 86 = 0.5349

Therefore 0.5349 is the required probability here.

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