Question 1196187
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In a certain school class, consisting of 60 girls and 40 boys, it is observed that 
24 girls and 16 boys wear eyeglasses. If a student is picked at random from this class, 
find the following probabilities:
a. the picked student is wearing eyeglasses.
b. the picked student is wearing eyeglasses and being a boy.
c. the picked student is wearing eyeglasses and not being a boy.
d. are the two events; wearing glasses and being a boy independent?
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<pre>
(a)  P = {{{wearing_glasses/total_students}}} = {{{(24+16)/(60+40)}}} = {{{40/100}}} = {{{4/10}}} = {{{2/5}}} = 0.4.



(b)  P = {{{the_number_of_boys_wearing_eyeglasses/total_students}}} = {{{16/100}}} = {{{4/25}}} = 0.16.



(c)  (Not being a boy) means (being a girl).  THEREFORE

     P = {{{the_number_of_girls_wearing_eyeglasses/total_students}}} = {{{24/100}}} = {{{6/25}}} = 0.24.



(d)  You should check if two numbers are equal:

         P(wearing glasses AND being a boy),     (1), 

     and

         P(wearing glasses)*P(being a boy)       (2)


     We have 

         P(wearing glasses AND being a boy) = {{{16/100}}}  for (1)

     and
         P(wearing glasses)*P(being a boy) = {{{(40/100)*(40/100)}}} = {{{(4/10)*(4/10)}}} = {{{16/100}}}  for (2).


     The numbers (1) and (2) are equal - - - hence, the events ARE independent.
</pre>

Solved.