A random experiment has four outcomes, A, B C and D, with
probabilities a,b, c and d , where d=1-a-b-c >0 and a>0,
b>0, C>0
What is the probability that, in a sequence of independent
performances of the
experiment, A will occur before D.
Here we have to find the probability that experiment A will occur before D.
that means in first chance, A will come or if B or C comes than A shall come in second chance and so on
P(A will occur Before D) = P(A comes first) + P(B or C comes first and A comes second) + P(B or C somes in first two chances and then A comes in third chance) + so on
= a + (b + c) a + (b + c)2a + (b + c)3 a
= a [1 + (b + c) + (b + c)2 + ..........]
= a [1/(1 - b -c)]
= a/(1 - b - c)
= a/(d +a)
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