5. 11 points DovoreStat9 2.E.038 My NotesO Ask Your Teacher An academic departme

Question

5. 11 points DovoreStat9 2.E.038 My NotesO 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)? Need Help?Read It Talk to a Tutor

Explanation / Answer

Let p=P[A] = 3/8 and q=P[B]=2/8.

The event that A will remain ahead of B if following vote count is realized;

AAABB or AABAB or BAAAB or ABAAB. It means that there four possibility of vote count will be in favor, and its probability is as follows;

Required Probability = P[AAABB} + P[AABAB] + P[BAAAB] + P[ABAAB]

                                      = 4 P[AAABB]

                                        = 4 P[A]3 P[B]2

                                          = 4 X (3/8)3 X (2/8)2

          =   0.013184

Which is approximately 0.013 = 13/1000

Means similarly kind of vote casting situation is performed 1000 times than in 13 situations A will remain ahead of B.

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