dauddastagir wrote:
I am not strong in probability formula. However, I have an option to look at the problem from a plain arithmetic point of view. First of all the president will be chosen. If Harry hasn’t been chosen as the president, then he has the chance to be eihter secretary or the treasurer. Given that, once someone other than Harry has already been chosen as the president, now 9 members are remaining from whom first the secretary will be chosen. Similarly when the secretary has already been chosen, then the treasurer will be chosen from the remaining 8 members. Therefore, Harry's chance to be the secretary is 1/9, thus his chance of being the treasurer is 1/8. From this logic, the average of 1/9 and 1/8 is 17/72.
I would really appreciate your help.
You can use probability rules to answer this question, though there are faster ways. For Harry to be chosen Secretary, two things need to happen: he must
not be chosen President, and then he must be chosen Secretary. When we need a sequence of things to happen, we multiply the probabilities of each thing. Harry will not be chosen President 9/10 of the time, and then will be chosen Secretary 1/9 of the time, as you correctly found. Multiplying, the probability he is Secretary is 9/10 * 1/9 = 1/10. Similarly, to be chosen Treasurer, he must not be President, and must not be Secretary, then must be chosen Treasurer, so the probability he is Treasurer is 9/10 * 8/9 * 1/8 = 1/10. Then to find the probability he is either Secretary or Treasurer, we do not average those two probabilities; we add them (as long as they can't both happen). So the answer is 2/10.
As I said earlier in the thread, I think there are better ways to think about the problem. Harry is just as likely as anyone else to be chosen Secretary, regardless of whether they choose Secretary first or second or last, so there must be a 1/10 chance that happens, and the same is true of the Treasurer position.