SOLUTION: In a city school, 60% of students have blue eyes, 55% have dark hair, and 20% have neither blue eyes nor dark hair. Determine the probability that a randomly selected student will

Question 1206867: In a city school, 60% of students have blue eyes, 55% have dark hair, and 20% have neither blue eyes nor dark hair. Determine the probability that a randomly selected student will have blue eyes and dark hair.

Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
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In a city school, 60% of students have blue eyes, 55% have dark hair,
and 20% have neither blue eyes nor dark hair. Determine the probability
that a randomly selected student will have blue eyes and dark hair.
~~~~~~~~~~~~~~~~~~~~~

Since  20%  have neither blue eyes nor dark hair, we conclude that 

100 -20% = 80% are those who either have blue eyes OR dark hair (or both).


So, now we have  that 60%  of students have blue eyes P(B) = 0.6, 
55% have dark hair  P(D) = 0.55,  and their union  (B U D)  is  80%:  P(B U D) = 0.8.


Having it and using basic formula of probability, we write

      P(B U D) = 0.8,

      P(B) + P(D) - P(B and D) = 0.8,

      0.6  + 0.55 - P(B and D) = 0.8,

      0.6 + 0.55 - 0.8 = P(B and D),

      P(B and D) = 0.35.


Therefore, the probability that a randomly selected student will have blue eyes and dark hair is

    P(B and D) = 0.35 = 35%.    ANSWER

Solved.

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