Question 252130
A box contains 2 green and 3 white balls. A ball is selected at random from the box. If the ball is green, a card is drawn from a deck of 52 ca rdto. If the ball is white, a card is drawn from the deck consisting of just the 16 pictures. 
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I don't get the "deck consisting of just the 16 pictures" since there are
only 12 picture cards (Jack, Queen and King of the 4 suits) in a standard deck
of 52. Perhaps this problem considers Aces to be picture cards. But I will
assume there are 16 picture cards anyway)
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(a) What is the probability of drawing a king? 
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P(green)={{{"P(G)"=2/5}}}
P(white)={{{"P(W)"=3/5}}}
P(king from deck of 52)={{{4/52=1/13}}}
P(king from 16 picture-card deck)={{{4/16=1/4}}}
P(green and king) = {{{"P(G&K)"}}}={{{(2/5)(1/13)=2/65}}}
P(white and king) = {{{"P(W&K)"}}}={{{(3/5)(1/4)=3/20}}}
P(king) = P(G&K OR W&K) = {{{2/65+3/20=47/260}}}
= {{{2/65+3/20=47/260}}}, about 18% of the time.
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(b) What is the probability of a white ball was selected given that a king was drawn?
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{{{"P(W|K)" = ("P(W&K)")/("P(K)")=(3/20)/(47/260)= (3/20)(260/47)=39/47}}}
or about 83% of the time.

Edwin<pre>