Indian Institute of Foreign Trade 2009 Solved Paper

Let x be the probability of investigation.
Let us indicate the event of the investigation happening to be I
=>Event of investigation not happening = I'
Similarly, let us indicate the event of importing the technology to be T
=> The event of technology not getting imported before the deadline = T'
The probability of Alpha getting the contract, Alpha's chances of getting a contract:-
1. If Gamma is able to import the technology and there is no investigation by the Government, P(A|I'&T)P(I'&T)=0.8×0.67×(1−x)
2. If there is investigation and Gamma Ltd is unable to import the technology in time, P(A|I&T')P(I&T') =0.72×0.2×x
3. If both events occur, P(A|I&T)P(I&T) =0.8×0.58×x
4. If none events occur,P(A|I'&T')P(I'&T')=0.85×0.2×(1−x)
The probability of the contract being awarded to Alpha Ltd is i.e. 0.056≥0.098x
i.e. 0.057≥x
Therefore, option B is the right answer