5. 11 points DevoreStat9 2.E.036 My Notes Ask Your Teacher An academic departmen

Question

5. 11 points DevoreStat9 2.E.036 My Notes Ask Your Teacher An academic department with five faculty members narrowed its choice for department head to either candidate A or candidate B. Each member then voted on a slip of paper for one of the candidates. Suppose there are actually three votes for A and two for B. If the slips are selected for tallying in random order, what is the probability that A remains ahead of B throughout the vote count (e.g., this event occurs if the selected ordering is AABAB, but not for ABBAA)?

Explanation / Answer

Total number of outcomes = 5!/(3!*2!) = 10

(AAABB), (AABAB), (AABBA), (ABABA), (ABAAB), (ABBAA), (BABAA), (BAAAB), (BAABA), (BBAAA)

Out of these only the first 2 are favourable (The third is not favourable as after the 4th slip they are tied)

Therefore the required probability = 2/10 = 1/5 = 0.2

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