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?

as a fraction	as a fraction in lowest terms
as a percent	as a decimal

b. place an \x\ where you think the theoretical probability of selecting a shaded tile belongs on the segment.
0% ---------------------------- 100%
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.
cuny start quantitative reasoning, class 20, version 2a

Explanation:

Step1: Count shaded and total tiles

First, we need to count the number of shaded tiles. From the image, we can see that there are 4 white tiles (the unshaded ones) and total tiles are 40. So shaded tiles = 40 - 4 = 36.

Step2: Theoretical Probability as a fraction

Theoretical probability of selecting a shaded tile is the number of shaded tiles divided by total number of tiles. So that's $\frac{36}{40}$.

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

To convert fraction to percent, multiply by 100. $\frac{9}{10} \times 100 = 90\%$.

Step5: Convert to decimal

To convert fraction to decimal, divide numerator by denominator. $\frac{9}{10}=0.9$.

(for part b):
The theoretical probability is $90\%$, so we place an "X" close to the $100\%$ mark, but at the $90\%$ position on the segment from $0\%$ to $100\%$.

(for part c):
Experimental probability is the number of times shaded tile was picked divided by total number of picks. Adenike picked a tile 22 (shaded) + 3 (white) = 25 times? Wait, wait, no, wait the problem says "picked a tile out of the bag 200 times"? Wait no, wait the first part: "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." Wait, so total picks are 22 + 3 = 25? Wait, that seems odd, but maybe. So experimental probability as a fraction is $\frac{22}{25}$. To convert to percent, $\frac{22}{25} \times 100 = 88\%$.

Wait, wait, let's check again. The problem says: "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." So total trials = 22 + 3 = 25. So experimental probability (shaded) = number of shaded picks / total picks = $\frac{22}{25}$. To convert to percent: $\frac{22}{25} \times 100 = 88\%$.

(for part d):
We use the theoretical probability (which is $\frac{9}{10}$ or $0.9$) and multiply by the number of trials (200). So number of times shaded tile is expected = theoretical probability × total trials = $0.9 \times 200 = 180$.

Answer:

(for part a):

• As a fraction: $\frac{36}{40}$
• As a fraction in lowest terms: $\frac{9}{10}$
• As a percent: $90\%$
• As a decimal: $0.9$

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