Question

1. the 40 tiles shown at the right were put into a sack, and the sack was shaken to mix them up. adenike picked a tile out of the bag at random a number of times (always recording the result and then putting the tile back). she counted that she picked a shaded tile 22 times and picked a white tile 3 times.

a. what is the theoretical probability of selecting a shaded tile out of the sack?

b. place an \x\ where you think the theoretical probability of selecting a shaded tile belongs on the segment.

c. determine the experimental probability of selecting a shaded tile out of the sack. show this probability as a fraction and also as a percent.

d. based on the theoretical probability, if we picked a tile from the sack 200 times (always putting the tile back in the bag and shaking up the tiles afterward), how many times would you estimate that we would pick a shaded tile? show how you figured this out.

Explanation:

Step1: Identify total and shaded tiles

Total tiles = 40, White tiles = 4, so shaded tiles = 40 - 4 = 36.

Step2: Calculate theoretical probability (fraction)

Theoretical probability = $\frac{\text{Shaded Tiles}}{\text{Total Tiles}}$ = $\frac{36}{40}$.

Step3: Simplify the fraction

Simplify $\frac{36}{40}$ by dividing numerator and denominator by 4: $\frac{36\div4}{40\div4}=\frac{9}{10}$.

Step4: Convert to percent

$\frac{9}{10} = 0.9$, and $0.9\times100\% = 90\%$.

Step5: Convert to decimal

$\frac{9}{10} = 0.9$.

For part d:

Step1: Use theoretical probability

Theoretical probability of shaded tile is $\frac{9}{10}$ (or 0.9).

Step2: Multiply by number of trials

Number of trials = 200, so estimated shaded picks = $200\times\frac{9}{10}$.

Step3: Calculate the result

$200\times\frac{9}{10} = 20\times9 = 180$.

Answer:

a. As a fraction: $\frac{36}{40}$; As a fraction in lowest terms: $\frac{9}{10}$; As a percent: $90\%$; As a decimal: $0.9$.
b. (Assuming the segment is from 0% to 100%, place X near 90% mark)
c. Fraction: $\frac{22}{25}$; Percent: $88\%$.
d. Estimated shaded tile picks: $180$ (calculated as $200\times\frac{9}{10}=180$).