Math Problem Statement
Can you help me modify my game ( Task 1
Game Name
Triple Challenge Treasures
Game Description:
Triple Challenge Treasures is a fun and exciting single-player game where players attempt three independent challenges (Challenge A, B, and C) to win various prizes. The more challenges a player successfully completes, the greater the prize they can win. However, if they fail all challenges, they walk away with nothing.
The game has an entry fee of $17 and offers three possible prize tiers based on how many challenges the player successfully passes:
· Small Prize for passing 1 challenge: $5
· Medium Prize for passing 2 challenges: $20
· Grand Prize for passing all 3 challenges: $60
Game Rules:
Entry Fee: The player pays an entry fee of $17 to play.
Challenges: The player must attempt any of these three challenges:
· Challenge A (Coin Flip): The player flips a coin and must get two consecutive heads to pass.
· Challenge B (Dice Roll): The player rolls a 12-sided die and must roll exactly 12 to pass.
· Challenge C (Card Draw): The player draws a card from a standard deck and must draw a red face card from diamonds (Jack, Queen, or King) to pass.) so that the provability distribution is some close to these values No Prize : 64.7 % Small Prize: 29 % Medium Prize: 7% Big Prize: 2.3 % So that when added up : 64.7 + 29 + 4 + 2.3 = 100 % (Or something close enough to be rounded up)
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Probability Distribution
Independent Events
Formulas
Combined probability for independent events: P(A and B and C) = P(A) * P(B) * P(C)
Probability of complementary events: P(not A) = 1 - P(A)
Theorems
Basic Probability Theorem for Independent Events
Suitable Grade Level
Grades 9-12
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