A jar contains 8 red, 3 purple and 7 black marbles. Four marbles are to be drawn in succession WITHOUT REPLACEMENT from the jar. Answer the questions which follow.
Be sure to differentiate in your answers those problems whose probability is ZERO versus those which CANNOT HAPPEN.
P(third marble is purple GIVEN first two were purple)
P(third marble is purple GIVEN first was red AND second was purple)
P( third marble is purple GIVEN first was black AND second was red)
P(third marble is purple GIVEN first three were black)
P(fourth marble is black GIVEN first three were NOT black)
P( fourth marble is red GIVEN first was red AND second was black AND third was purple)
P(fourth marble is purple GIVEN first three were purple)
P( fourth marble is NOT red GIVEN first was red AND second was purple AND third was black)
P( all four marbles were black)
P(first AND second were red AND third AND fourth were purple)
P(none were purple)
P( first was not red AND second was black AND last two were purple)
P( first was black AND second was NOT purple AND third was NOT black AND fourth was red)
P(all marbles were the same color)
A jar contains 8 red, 3 purple and 7 black marbles. Four marbles are to be drawn in succession WITHOUT REPLACEMENT from the jar. Answer the questions which follow.
Be sure to differentiate in your answers those problems whose probability is ZERO versus those which CANNOT HAPPEN.
P(third marble is purple GIVEN first two were purple)
P(third marble is purple GIVEN first was red AND second was purple)
P( third marble is purple GIVEN first was black AND second was red)
P(third marble is purple GIVEN first three were black)
P(fourth marble is black GIVEN first three were NOT black)
P( fourth marble is red GIVEN first was red AND second was black AND third was purple)
P(fourth marble is purple GIVEN first three were purple)
P( fourth marble is NOT red GIVEN first was red AND second was purple AND third was black)
P( all four marbles were black)
P(first AND second were red AND third AND fourth were purple)
P(none were purple)
P( first was not red AND second was black AND last two were purple)
P( first was black AND second was NOT purple AND third was NOT black AND fourth was red)
P(all marbles were the same color)
Be sure to differentiate in your answers those problems whose probability is ZERO versus those which CANNOT HAPPEN.
P(third marble is purple GIVEN first two were purple)
P(third marble is purple GIVEN first was red AND second was purple)
P( third marble is purple GIVEN first was black AND second was red)
P(third marble is purple GIVEN first three were black)
P(fourth marble is black GIVEN first three were NOT black)
P( fourth marble is red GIVEN first was red AND second was black AND third was purple)
P(fourth marble is purple GIVEN first three were purple)
P( fourth marble is NOT red GIVEN first was red AND second was purple AND third was black)
P( all four marbles were black)
P(first AND second were red AND third AND fourth were purple)
P(none were purple)
P( first was not red AND second was black AND last two were purple)
P( first was black AND second was NOT purple AND third was NOT black AND fourth was red)
P(all marbles were the same color)
P(third marble is purple GIVEN first two were purple) = (3/18)*(2/17)*(1/16) / [(3/18) * (2/17)] = 1/16......
P(third marble is purple GIVEN first was red AND second was purple)
= (8/18)*(3/17)*(2/16) / [ (8/18) * ( 3/17) ] = 2/16 = 1/8....
P( third marble is purple GIVEN first was black AND second was red) = 3/16...
P(third marble is purple GIVEN first three were black) = cannot happen..
P(fourth marble is black GIVEN first three were NOT black) = 7/15....
P( fourth marble is red GIVEN first was red AND second was black AND third was purple)= 7/15...
P(fourth marble is purple GIVEN first three were purple) = 0.....
P( fourth marble is NOT red GIVEN first was red AND second was purple AND third was black) = 8/15...
P( all four marbles were black) = 7*6*5*4 / [18*17*16*15] = 0.0114379...
P(first AND second were red AND third AND fourth were purple) = (8/18)*(7/17)*(3/16)*(2/15) = 0.004575163...
P(none were purple) = (15/18) * (14/17 )* (13/16) * (12/15) = 0.4460784.....
P( first was not red AND second was black AND last two were purple)
=[ (3/18)*(7/17)*(2/16)*(1/15) + (7/18)*(6/17)*(3/16)*(2/15) ] = 0.004003268....
P( first was black AND second was NOT purple AND third was NOT black AND fourth was red)
= (7/18)*(6/17)*( 8 /16)*( 7/15) + (7/18)*(6/17)*(3/16)*(8/15) + (7/18)*(8/17)*(3/16)*(7/15) + ( 7/18)*(8/17)*(7/16)*(6/15) = 0.09379085.....
P(all marbles were the same color)
= (8/18)*(7/17)*(6/16)*(5/15) + (7/18)*(6/17)*(5/16)*(4/15) = 0.03431373......
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