Question 1207265
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An urn contains 7 red marbles, 6 white marbles, and 8 blue marbles. 
A child randomly selects three (without replacement) from the urn. 
Round to four decimal places.

(a)Find the probability all three marbles are the same color.

(b) Find the probability that none of the three marbles are white.
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(a)  In (a), the probability is the sum of the probabilities of three disjoint events:

     P = P(all three marbles are red) + P(all three marbles are white) + P(all three marbles are blue) = 

       = {{{(7/21)*(6/20)*(5/19)}}} + {{{(6/21)*(5/20)*(4/19)}}} + {{{(8/21)*(7/20)*(6/19)}}} = 0.0835  (rounded).


     Here  21 = 7 + 6 + 8 is the total marbles.


     The structure of the formula is clear, and the structure reflects its meaning.



(b)  P = {{{(15/21)*(14/20)*(13/19)}}} = 0.3421  (rounded).


     Here  15 = 7+8  is the number of all non-white marbles.


     Again, the structure of the formula is clear, and the structure reflects its meaning.
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Solved.