Suppose the two events “high” and “low” make a disjoint partition of a sample space and “favourable” is any event. If P(high) = 0.3, P(low) = 0.7, P(favourable| high) = 0.9 and P(unfavorable| low) = 0.6, then P(favourable) is
Answer given for this quesiton is 0.55
My approach:
All I know is that P(A|B) = P(A∩B) / P(B)
so may be we can take (favorable∩0.3)/P(0.3) = 0.9
I do not know how to solve it. Please help me on how to get the value of P(Favorable).
\begin{eqnarray*} P\left(F\right) &=& P\left(F\vert H\right)P\left(H\right) + P\left(F\vert L\right)P\left(L\right) \\ &=& P\left(F\vert H\right)P\left(H\right) + \left(1 - P\left(U\vert L\right)\right)P\left(L\right) \\ &=& 0.9 \times 0.3 + \left(1 - 0.6\right) \times 0.7 \\ &=& 0.27 + 0.28 \\ &=& 0.55 \end{eqnarray*}