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posted by  Iriene on 2/12/2008 12:32:06 AM  |  status: Live  

Discrete Maths.Construct the Tree Diagram

Course Textbook Chapter Problem
Discrete Math N/A N/A N/A
Question Details:

Construct the tree diagram of the following:

Ali has time to play roulette at most five times. At each play he wins or loses 1 point. He begins with 1 point and will stop playing before the five times if he loses all his points or if he wins 3 points that is, if he has 4 points.

Find the number of ways the betting can occur, and find the number of times he will stop before betting five times.

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posted by gomorycut on 2/13/2008 1:44:48 AM  |  status: Live
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Iriene's comment:
"Thanks a lot.You saved our skins SIR"
Response Details:
The question asks for a tree diagram. So we will start at the root of the tree and he begins with 1 points. Then every step from there he can win or lose. We stop the tree if his points reach 0 or if he gets 4 points.
 
 
 
So the tree shows that he could possibly stop before playing 5 times in 4 different ways. The total number of ways betting can occur is the number of endpoints  = 11.

Feel free to send me a private message with any followup questions if there is something you want clarified or re-explained.
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posted by sajid on 2/13/2008 6:12:05 AM  |  status: Live
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Iriene's comment:
"Thanks But in the last round its 02240224.Please correct it"
Response Details:
Exit conditions: Points = 0 or 4

Total Points round zero 1
/ \
Total Points round one 0 2
/ \
Total Points round two 1 3
/ \ / \
Total Points round three 0 2 2 4
/ \ / \
Total Points round four 1 3 1 3
/ \ / \ / \ / \
Total Points round five 0 2 1 4 0 2 1 4

Thus number of ways betting can occur =
1 (exit round 1) + 2 (exit round 3) + 8 (total round 5)
= 11

Number of exit points (number of times reach 0 or 4) = 7
sajidscoropio
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