SOLUTION: 1.Roll two six-sided dice. Add the face values together.
2.Choose whether to roll the dice again or pass the dice to your opponent.
3.If you pass, then write down your current to
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Probability-and-statistics
-> SOLUTION: 1.Roll two six-sided dice. Add the face values together.
2.Choose whether to roll the dice again or pass the dice to your opponent.
3.If you pass, then write down your current to
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Question 714893: 1.Roll two six-sided dice. Add the face values together.
2.Choose whether to roll the dice again or pass the dice to your opponent.
3.If you pass, then write down your current total. If you roll again, then add your result to your previous score.
4.Continue to roll as much as you want. However, once a 1 comes up on either die, your score is reduced to 0 and you must pass the dice to your opponent.
4. Continue to roll as much as you want. However, once a 1 comes up on either die, your score is reduced to 0 and you must pass the dice to your opponent.
The first person to 100 points is the winner. To help with the probabilities and averages in this problem, you may want to write down all the possible outcomes.
P(A): ?
P(B): ?
Looking at your table above, what is the mean value of a successful roll????
What is the value added to your score when you have a failed roll? ???/
Strategy: Roll once then pass
P(successfully rolling once):
P(failure):
Points for one successful roll:
Expected value:
Strategy: Roll twice then pass
P(successfully rolling once):
P(failure):
Points for one successful roll:
Expected value:
Strategy: Roll three times then pass
P(successfully rolling once):
P(failure):
Points for one successful roll:
Expected value:
Strategy: Roll four times then pass
P(successfully rolling once):
P(failure):
Points for one successful roll:
Expected value:
Strategy: Roll five times then pass
P(successfully rolling once):
P(failure):
Points for one successful roll:
Expected value:
Which strategy would you use? Why?
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