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QUESTION

# The 300 voting residents of Gator Hollow, Florida, are electing a new mayor. Whoever gets the most votes wins. The three candidates are named Dubya,...

The 300 voting residents of Gator Hollow, Florida, are electing a new mayor. Whoever gets the most votes wins. The three candidates are named Dubya, Patrick, and Albert. Being in rural Florida, the election is somewhat unique:

• 140 of the residents (including Dubya) plan to vote for Dubya. All will be  able to do so successfully.
• 10 of the residents (including Patrick) plan to vote for Patrick. All will be   able to do so successfully.
• 150 of the residents (including Albert) plan to vote for Albert. Of these, 130 will be able to do so successfully. The remaining 20 are, shall we say, intellectually challenged and are having difficulty understanding the ballot. They each have an equal and independent 40 percent chance of unintentionally voting for Patrick.

a)   What is the probability that Albert is elected mayor?

b)   What is the probability that Dubya is elected mayor?

c)   What is the probability that the election results in a dead-heat (a tie) between Albert and Dubya?