Question

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.

Answer 1

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)