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A bag contains 5 red marbles and 3 black marbles.Three marbles are drawn one by one with out replacement.What is the probability that at least one of the three marbles drawn be black,if the first marble is red?

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  • let\((E_1)\)be the event 1st marble is red
  • \((E_2)\)at least one is black
  • First marble is red can occur in following ways
  • \((E_1)\)={\(R\;B\;B)(R\;B\;R)(R\;R\;B)(R\;R\;R)\)}
  • At least one black
  • \((E_2)\)={\(B\;B\;B)(B\;R\;B)(B\;B\;R)(B\;B\;R)(R\;B\;B)(R\;B\;R)(R\;R\;B)\)}
  • \((E_1\;\cap\;E_2)\)={\(R\;B\;R)(R\;B\;B)(R\;R\;B)\)}
There are 5R and 3B marbles
We can also do
P(first ball is red)=\(\large\frac{5}{8}\)
P\((E_2)\)=P(at least 1 black)
=1-P(no black)
Requier probability=\(\large\frac{25}{56}\times\)\(\large\frac{8}{5}\)


answered Feb 24, 2013 by poojasapani_1
edited Jun 5, 2013 by poojasapani_1

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