9 The table provides the gender distribution of 200203 PCC G

9. The table provides the gender distribution of 2002-03 PCC Gender Distribution Across Programs PCC students across the different programs offered at PCC. Answer the following questions based on Male Female Total the table. Write each question posed in function Lower Division Transfer 12866 B159 ET025 notation. Round answers to the ten-thousandths 16216 12222 2A438 Professional Technical unit. Developmental Education 66 682 1338 Adult Education 3962 4368 8330 Total 33700 35431 69131 la. [4] (1) What is probability of choosing a PCC student at random and having that student be female? lb. [4] A student is chosen at random from the PCC population. Given that the student is classified as lower division transfer student, what is the probability of that student being female? lc. [4] (1) Are the events \"a student is a female\", and \"a person is in the lower division transfer program\" independent? You must show work that supports the answer in order to get credit.

Solution

a)

P(female) = 35431 / 69131 = 0.5125

b)

P(female | lower division) = 18159 / (totla in lower division)

18159 / 31025

0.5853

c)

P(female) = 35431/69131 = 0.5125
P(lower division) = 31025/69131 = 0.4488
P(female and lower division) = 18159/69131 = 0.2627

Now, for independent events :
P(female) * P(lower division) = P(female and lower division)
Let us see if this is true or not

0.5125 * 0.4488 =0.23001 not equal to 0.2627

So, proven that the events \"female\" and \"lower division\" are not independent