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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)?

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The probability that the first two votes drawn are both for candidate a is given by:
3C2/5C2 = 3/10
Having drawn two votes for candidate a on the first two draws, there are 2 votes for candidate b and one vote for candidate a remaining. The probability that a vote for candidate b will be drawn on the third draw is:
2/3.
After the first three draws, there reains one vote for candidate a and one vote for candidate b. The probability that a vote for candidate a will be drawn on the fourth draw is:
1/2.
The probability of the ordering aabab is therefore given by:
[tex]\frac{3}{10}\times\frac{2}{3}\times\frac{1}{2}=\frac{6}{60}[/tex]
The answer is: 0.1.

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