The Board of Directors of a small company consists of five people. Two of those directors are considered "strong leaders". If th
ey like an idea, the entire board will agree. The three remaining directors have no influence. Three sales people are scheduled, one after another, to make a sales presentation to a single board member of the salesperson's choice. The sales people are all convincing but do not know who the "strong leaders" are. However, they will know who the previous sales person spoke to. The first sales person to find a strong leader will win the sale. Do the three sales people all have the same chance of winning the account? If not, what are the three respective probabilities for winning the account?
If we know one of the succeeded, then 1: 44.44% 2: 33.33% 3: 22.22%
If under the circumstance that they all fail to meet a strong leader, the board picks one of them at random, 1: 43.33% 2: 33.33% 3: 23.33%
The first person has a 2 in 5 chance of randomly getting a strong leader. If the first person doesn't find a strong leader, the second person has a 2/4 chance of getting a strong leader. If neither the first nor second person gets a strong leader, the third sales person has a 2/3 chance of getting a strong leader.
1: 2/5=40% Chance 2: (3/5)*(2/4)=30% Chance You have to take the probability the first rep failed to get a strong leader, then multiply by the probability the second rep gets a strong leader. 3: (3/5)*(2/4)*(2/3)=20% You have to take the probability both the other people failed, then multiply by the probability they succeeded.
