MHB Roll the Die: Win \$10 or Lose \$2?

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The game involves rolling a balanced six-sided die, where rolling a one wins $10 and any other result loses $2. The two possible outcomes are winning $10 with a probability of 1/6 and losing $2 with a probability of 5/6. To determine if paying $2 to play is worthwhile, one must calculate the expected value by multiplying each outcome by its probability and summing the results. The expected value calculation reveals whether the game is favorable or not. Understanding these probabilities and expected outcomes is essential for making an informed decision about playing the game.
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someone help me understand these questions please:
1) Would you pay \$ 2 to play this game? if you throw a one on a balanced die, you receive \$10, otherwise you lose you \$2.
a) what are the two possibilities for this game?
b) what are the corresponding probabilities associated with these possibilites? and would you pay 2 dollars to play this game?
 
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lilly said:
someone help me understand these questions please:
1) Would you pay \$ 2 to play this game? if you throw a one on a balanced die, you receive \$10, otherwise you lose you \$2.
a) what are the two possibilities for this game?
b) what are the corresponding probabilities associated with these possibilites? and would you pay 2 dollars to play this game?

Welcome to MHB lilly! :)

The two possibilities are that either you win \$10 or you lose \$2.

A balanced die is a die with 6 sides that each have the same probability of coming up.
So the probability on a one is 1/6.

How much do you think you would earn if you play this game?
This is called "expected value".
To find it you need to multiply the probabilities with the outcomes and add them up.
What do you think it is?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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