SOLUTION: 7. A class of 16 pupils consist of 10 girls, 3 of whom are left-handed, and 6 boys, only one of whom is left-handed. The two pupils are to be chosen at random from the class to act

Question 1192084: 7. A class of 16 pupils consist of 10 girls, 3 of whom are left-handed, and 6 boys, only one of whom is left-handed. The two pupils are to be chosen at random from the class to act as monitors. Calculate the probabilities that the chosen pupils will consist of
i. One girl and one boy
ii. One girl who is left-handed and one boy who is left-handed.
iii. Two left- handed pupils.

Answer by ikleyn(52864) (Show Source): You can put this solution on YOUR website!
.
7. A class of 16 pupils consist of 10 girls, 3 of whom are left-handed,
and 6 boys, only one of whom is left-handed.
The two pupils are to be chosen at random from the class to act as monitors.
Calculate the probabilities that the chosen pupils will consist of
a. One girl and one boy
b. One girl who is left-handed and one boy who is left-handed.
c. Two left- handed pupils.
~~~~~~~~~~~~~~~~~

(a)  The number of different pairs of pupils is   = 8*15 = 120.

     The number of different pairs (girl,boy) is 10*6 = 60.

     Therefore, the probability that an arbitrary pair will consist of a boy and a girl is

          P =  =  = 0.5 = 50%.



(b)  The number of different pairs (left-handed girl,left-handed boy) is 3*1 = 3.

     Therefore, the probability that an arbitrary pair will consist of a left-handle girl and a left handled boy is

          P =  = .



(c)  The total of left handed pupils is 3+1 = 4.  The number of left-handled pairs is   = 2*3 = 6.

     Therefore, the probability that an arbitrary pair will consist of left-handled pupils is

          P =  = .

Solved.

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