This question was asked in an interview for software developer and I was unable to figure out the complete solution please help to solve this question for future.

The Israelis MOSAD group has n Assassin for the role of Killing ISIS Terrorists, who help in smooth killing of Terrorists who intruded in their country. Every Agents can either manage to shoot a terrorist or miss it.

Out of these n Killing Assassins, m assassins try to shoot the terrorist fairly, that is, they are unbiased, while the rest of them are biased. The probability that a terrorist will be hit by a shot if the Killing Assissin is biased is 2/3, otherwise the probability is 1/2.

Now MOSAD Chief figures out this mess by selecting a Killing Assassin randomly. He tricks that particular Killing Assassin in shooting the same terrorist twice. The first time, the Killing Assassin shoots the terrorist, while the other time, he ends up missing it.

Chief wants to know what are the chances that the selected Killing Assistant was NOT biased.

Given data is Total number of assassin is 8 and out of 8, 5 are unbiased assassins.

Answers may be one of the option
1) 15/23
2) 17/49
3) 1/1
4) 14/19

• option (1)
  
  number of total events= (5/8)*(1/2)*(1/2) [ probability of selecting unbiased assassins * probability of shooting terrorist * probability of missing terrorist] + (3/8)*(2/3)*(1/3) [ probability of selecting biased assassins * probability of shooting terrorist * probability of missing terrorist] = 23/96
  
  favourable case = 5/8 * 1/2 * 1/2 ( selecting an unbiased)=5/32
  
  probability = (5/32)/(23/96)=15/23
• 6 years agoHelpfull: Yes(0) No(0)