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

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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(53937) About Me  (Show Source):
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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?
~~~~~~~~~~~~~~~~~~~~~ 

(a)  P = wearing_glasses%2Ftotal_students = %2824%2B16%29%2F%2860%2B40%29 = 40%2F100 = 4%2F10 = 2%2F5 = 0.4.



(b)  P = the_number_of_boys_wearing_eyeglasses%2Ftotal_students = 16%2F100 = 4%2F25 = 0.16.



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

     P = the_number_of_girls_wearing_eyeglasses%2Ftotal_students = 24%2F100 = 6%2F25 = 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%2F100  for (1)

     and
         P(wearing glasses)*P(being a boy) = %2840%2F100%29%2A%2840%2F100%29 = %284%2F10%29%2A%284%2F10%29 = 16%2F100  for (2).


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

Solved.