SOLUTION: 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

Question 1196187: 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?
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
..
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?
~~~~~~~~~~~~~~~~~~~~~

(a)  P =  =  =  =  =  = 0.4.



(b)  P =  =  =  = 0.16.



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

     P =  =  =  = 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) =   for (1)

     and
         P(wearing glasses)*P(being a boy) =  =  =   for (2).


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

Solved.

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