Question

type the correct answer in each box. spell all words correctly.
jason organized three games at a school carnival.

• carnival wheel is a game in which the player spins a wheel with seven equal - sized sections, each of a different color. the player wins if the wheel lands on the violet section.
• bingo ball is a game in which the player picks a ball from a box of ten balls, each of a different color. the player wins if the white ball is picked.
• dice to win is a game in which the player rolls a six - sided die. the player wins if the die lands on 6.

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

type \true\ or \false\ after each statement below.
the results from game a align closely with the theoretical probability of winning that game.
the results from game b align closely with the theoretical probability of winning that game.
the results from game c align closely with the theoretical probability of winning that game.

Explanation:

Step1: Calculate theoretical probabilities

• Carnival Wheel (A): There are 7 equal - sized sections. The theoretical probability of winning \(P(A)=\frac{1}{7}\approx0.143\). The experimental probability \(P_{exp}(A)=\frac{26}{26 + 149}=\frac{26}{175}\approx0.149\)
• Bingo Ball (B): There are 10 balls. The theoretical probability of winning \(P(B)=\frac{1}{10}=0.1\). The experimental probability \(P_{exp}(B)=\frac{82}{82+118}=\frac{82}{200}=0.41\)
• Dice to Win (C): There are 6 sides on a die. The theoretical probability of winning \(P(C)=\frac{1}{6}\approx0.167\). The experimental probability \(P_{exp}(C)=\frac{39}{39 + 201}=\frac{39}{240}=0.1625\)

Step2: Compare experimental and theoretical probabilities

• For game A: \(\vert0.149 - 0.143\vert=0.006\)
• For game B: \(\vert0.41-0.1\vert = 0.31\)
• For game C: \(\vert0.1625 - 0.167\vert=0.0045\)

Answer:

True, False, True