Consider the following game: You start with $1. The game is over when you run out...

Consider the following game:

You start with $1. The game is over when you run out of money.

You flip a coin-----Heads means that you win $1 and Tails means that you lose $1

What is the probability that the game will end after:

a. 1 flip of the coin?

b. 2 flips of the coin?

c. 3 flips of the coin?

d. 4 flips of the coin?

You can set up a tree diagram.

You can show your explained calculations

You can set up a chart.

Just make sure that you show or explain how you arrived at your answer.

Solutions

Expert Solution

You start with $1. The game is over when you run out of money.

You flip a coin-----Heads means that you win $1 and Tails means that you lose $1

a. probability that the game will end after 1 flip of the coin

=> 1st flip should be tail so that $1 is lost and nothing is left

Probability = 1/2 = 0.5

b. probability that the game will end after 2 flips of the coin

There is no combination for which you will end with no money after 2 flips

Thus, required Probability = 0

c. probability that the game will end after 3 flips of the coin

=> Only combination is Head,Tail,Tail in given order (If first is Tail then the game is over there itself)

Probability = 1/2*1/2*1/2 = 1/8 = 0.125

d. probability that the game will end after 4 flips of the coin

There is no combination for which you will end with no money after 4 flips

Thus, required Probability = 0

Number of Flips	1	2	3	4
P(Game over)	0.5	0	0.125	0

milcah answered 5 months ago

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