Question

rick organized three games for a clubs 25th anniversary celebration.
a. get - it - rolling is a game in which the player rolls an eight - sided die. the player wins if the die lands on 5.
b. bag - of - tokens is a game in which the player draws a token from a bag containing 7 tokens, each of a different color. the player wins if they draw the red token.
c. pick - your - tile is a game in which the player picks a number tile from a box of 12 tiles, each with a different number on it. the player wins if they pick the tile that has the number 9 on it.
rick kept track of wins and losses for each game attempt in the following table

select the correct statement
a. only the results from game b align closely with the theoretical probability of winning that game.
b. the results from both game a and game c align closely with the theoretical probability of winning those games, while the results from game b do not.
c. the results from both game b and game c align closely with the theoretical probability of winning those games, while the results from game a do not.
d. only the results from game a align closely with the theoretical probability of winning that game

Explanation:

Step1: Calculate theoretical probability

• Game A: An eight - sided die, theoretical probability of winning \(P(A)=\frac{1}{8}=0.125\). Experimental probability \(P_{exp}(A)=\frac{26}{26 + 173}=\frac{26}{199}\approx0.131\)
• Game B: 7 tokens, theoretical probability of winning \(P(B)=\frac{1}{7}\approx0.143\). Experimental probability \(P_{exp}(B)=\frac{54}{54+141}=\frac{54}{195}\approx0.277\)
• Game C: 12 tiles, theoretical probability of winning \(P(C)=\frac{1}{12}\approx0.083\). Experimental probability \(P_{exp}(C)=\frac{17}{17 + 175}=\frac{17}{192}\approx0.089\)

Step2: Compare probabilities

• For game A: \(|0.131 - 0.125|=0.006\)
• For game B: \(|0.277-0.143| = 0.134\)
• For game C: \(|0.089 - 0.083|=0.006\)

Answer:

B. The results from both game A and game C align closely with the theoretical probability of winning those games, while the results from game B do not.