Question

rick kept track of wins and losses for each game attempt in the following table.

game	get - it - rolling (a)	bag - of - tokens (b)	pick - your - tile (c)
number of losses	173	141	175

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.
select the correct statement.
a. 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.
b. only the results from game a align closely with the theoretical probability of winning that game.
c. only the results from game b align closely with the theoretical probability of winning that game.
d. 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.

Explanation:

Step1: Calculate theoretical probabilities

For Get - It - Rolling (A), probability of winning is $\frac{1}{8}$ since there is 1 favorable outcome (rolling a 5 on an eight - sided die) out of 8 possible outcomes. For Bag - of - Tokens (B), probability of winning is $\frac{1}{7}$ as there is 1 favorable token out of 7. For Pick - Your - Tile (C), probability of winning is $\frac{1}{12}$ as there is 1 favorable tile out of 12.

Step2: Calculate experimental probabilities

For game A, experimental probability of winning $P(A)=\frac{26}{26 + 173}=\frac{26}{199}\approx0.131$. For game B, experimental probability of winning $P(B)=\frac{54}{54+141}=\frac{54}{195}\approx0.277$. For game C, experimental probability of winning $P(C)=\frac{17}{17 + 175}=\frac{17}{192}\approx0.089$.

Step3: Analyze alignment

The experimental probability of game B ($\approx0.277$) is relatively close to its theoretical probability ($\frac{1}{7}\approx0.143$) compared to the other games. The experimental probability of game A ($\approx0.131$) and game C ($\approx0.089$) do not align as closely with their theoretical probabilities.

Answer:

B. Only the results from game A align closely with the theoretical probability of winning that game.