Question

which experimental result best matches the theoretical probability of the event?
a. sarah spins a spinner with 6 equal - sized sections of different colors and records the color on which the spinner lands. she repeats this 24 times. the results show that the spinner landed on red 10 times.

b. mia has a bag that contains a letter block for each of the 26 letters of the alphabet. she draws a letter block from the bag, writes down the letter, and puts the block back in the bag. she repeats this 26 times. the results show that she drew a vowel (a, e, i, o, or u) 6 times.

c. charlie draws a number tile from a box containing the numbers 1 to 10, writes down the number, and puts the tile back in the box. he repeats this 40 times. the results show that the number 5 was drawn 10 times.

d. liza has an 8 - sided number solid that is numbered 1 through 8. she rolls it 56 times and records her results. the results show that an even number was rolled 14 times.

Explanation:

Step1: Calculate theoretical probability (A)

Theoretical probability of red: $\frac{1}{6} \approx 0.1667$
Expected red spins: $24 \times \frac{1}{6} = 4$
Difference: $|10 - 4| = 6$

Step2: Calculate theoretical probability (B)

Theoretical probability of vowel: $\frac{5}{26} \approx 0.1923$
Expected vowel draws: $26 \times \frac{5}{26} = 5$
Difference: $|6 - 5| = 1$

Step3: Calculate theoretical probability (C)

Theoretical probability of 5: $\frac{1}{10} = 0.1$
Expected 5 draws: $40 \times \frac{1}{10} = 4$
Difference: $|10 - 4| = 6$

Step4: Calculate theoretical probability (D)

Theoretical probability of even: $\frac{4}{8} = 0.5$
Expected even rolls: $56 \times 0.5 = 28$
Difference: $|14 - 28| = 14$

Answer:

B. Mia has a bag that contains a letter block for each of the 26 letters of the alphabet. She draws a letter block from the bag, writes down the letter, and puts the block back in the bag. She repeats this 26 times. The results show that she drew a vowel (A, E, I, O, or U) 6 times.