A $100 note is hidden in one of the 10 gift boxes, while the other nine boxes ar
ID: 3125611 • Letter: A
Question
A $100 note is hidden in one of the 10 gift boxes, while the other nine boxes are empty. Alice and Bob keep choosing one box at a time alternatively and open it. Once the box with the note is opened, the money belongs to the person who's picked the box. Who has a better chance to own the 100 note? The player who picks the first box. or the other one? Let Alice chooses the first box, and Bob opens the second one (if the first box is empty), and so on. What is chance that Alice wins in her first attempt? What is the probability that Bob wins in his first turn? Compute the probability that Alice wins in her second choice. Compute the probability that Alice eventually wins the game. What is the probability that Bob eventually wins the game. Answer to part (a) again. Is your initial guess supported by your calculations? Explain.Explanation / Answer
The player who picks the first box or second box has same probability of winning the $100 note .
The probability of winning the first box is 1/10.
The probability of winning Alice in her first attempt is 0.1
The probability of winning Bob is 0.1 r 1/10
The probability of winning Alice in her second choice is 0.8 r 8/10.
The probability of winning Alice is 1/2.
The probability of winning Bob is 1/2.
Yes guess with probability of 1/10
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