Question 924352
15 marbles: 3Y, 4W, 8B
Two marbles are drawn w/o replacement
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P(at least one yellow marble) = 1 - P(no yellow) = 1 - {{{(12/15)(11/14)}}}
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P(at most one yellow marble) = Y1st + Y2nd = {{{ (3/15)(12/14) + (12/15)(3/14)= 72/(14*15))  }}}
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P(both marbles are the same color) = 2Y+2W+2R = {{{ (3/15)(2/14) + (4/15)(3/14) + (8/15)(7/14) = 74/(14*15)}}}
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P(B and W) = {{{ (8/15)(4/14) + (4/15)(8/14)= 64/(14*15))  }}}
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P(marbles are of two different colors) = 1 - P(same color) = 1 - {{{74/(14*15)}}}