Mr. Raheja, the president of Alpha Ltd., a construction company, is studying his company’s chances of being awarded a Rs. 1,000 crore bridge building contract in Delhi. In this process, two events interest him. First, Alpha’s major competitor Gamma Ltd, is trying to import the latest bridge building technology from Europe, which it hopes to get before the deadline of the award of contact. Second, there are rumors that Delhi Government is investigating all recent contractors and Alpha Ltd is one of those contractors, while Gamma Ltd is not one of those. If Gamma is able to import the technology and there is no investigation by the Government, then Alpha’s chance of getting contract is 0.67. If there is investigation and Gamma Ltd is unable to import the technology in time, the Alpha’s chance is 0.72. If both events occur, then Alpha’s chance of getting the contract is 0.58 and if none events occur, its chances are 0.85. Raheja knows that the chance of Gamma Ltd being able to complete the import of technology before the award date is 0.80. How low must the probability of investigation be, so that the probability of the contract being awarded to Alpha Ltd is atleast 0.65? (Assume that occurrence of investigation and Gamma’s completion of import in time is independent to each other.)