three persons A,B andC draw in succession from a bag containing 8silver and 4 gold coins until a gold coin is drawn.what is the probability that C draws a gold coin?
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A, B and C will draw from the bag until a gold coin is drawn i.e. when a gold coin is drawn the action stops. For C to draw a gold coin both A and B should not have taken gold coins i.e. they should have taken silver coins.
Probability of A getting a silver coin = 8/12
Since A has already drawn a silver coin there is one less coin in the bag so,
Probability of B getting a silver coin = 7/11
Now, there are 2 less coins in the bag of which 4 are golden.
Probability of C getting a gold coin = 4/10
Since these three events should happen in success for the desired outcome,
Probability = 8/12 * 7/11 * 4/10
= 28/165
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