Math worksheet asking students to calculate experimental probability based on a sample of 20 socks picked from a drawer.

Let’s solve this step by step.

We are told that you randomly picked 20 socks from your drawer, and here’s what you got:

- White: 12
- Blue: 1
- Black: 3
- Tan: 4

Total = 12 + 1 + 3 + 4 = 20 socks (matches the problem)

You know there are 64 total individual socks in the drawer (since 32 pairs × 2 = 64).

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Part A: Experimental Probability

Experimental probability = (number of times event happened) / (total number of trials)

So for each color:

- P(white) = 12/20 → simplify: divide numerator and denominator by 4 → 3/5
- P(blue) = 1/20 → already simplified → 1/20
- P(black) = 3/20 → already simplified → 3/20
- P(tan) = 4/20 → simplify: divide by 4 → 1/5

✔ So:

P(white) = 3/5
P(blue) = 1/20
P(black) = 3/20
P(tan) = 1/5

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Part B: Predict how many socks of each color are in the drawer

We use the experimental probabilities to predict how many of the 64 total socks are each color.

Multiply each probability by 64:

- White: (3/5) × 64 = (3 × 64) / 5 = 192 / 5 = 38.4 → but we can’t have 0.4 of a sock! Hmm… let’s check if we should round or keep as fraction? The problem says “predict”, so maybe we round to nearest whole number? But wait — let’s see what the actual numbers are later. For now, let’s do exact math first.

Actually, since we’re predicting based on sample, it’s okay to get decimals at first, then round reasonably. But let’s think: 38.4 is close to 38 or 39? Let’s hold off rounding until we check consistency.

Wait — maybe better to use proportions directly from the sample.

In the sample of 20 socks:

- White: 12 out of 20 → so proportion = 12/20 = 3/5 → same as above.
→ 3/5 of 64 = 38.4 → perhaps we’ll say 38 or 39? But let’s look at others.

Blue: 1/20 × 64 = 64/20 = 3.2 → about 3

Black: 3/20 × 64 = 192/20 = 9.6 → about 10

Tan: 4/20 × 64 = 256/20 = 12.8 → about 13

Now add them up: 38.4 + 3.2 + 9.6 + 12.8 = 64 → perfect!

But since we can’t have fractions of socks, we need to assign whole numbers that add to 64.

Let’s try rounding:

White: 38.4 → 38
Blue: 3.2 → 3
Black: 9.6 → 10
Tan: 12.8 → 13

Sum: 38 + 3 + 10 + 13 = 64 ✔ Perfect!

So predicted number of individual socks:

White = 38
Blue = 3
Black = 10
Tan = 13

Wait — but let’s double-check with another method.

Alternative: Use ratio from sample.

Sample ratios:

White : Blue : Black : Tan = 12 : 1 : 3 : 4

Total parts = 12+1+3+4 = 20 parts

Each part represents 64 / 20 = 3.2 socks

Then:

White: 12 × 3.2 = 38.4 → 38
Blue: 1 × 3.2 = 3.2 → 3
Black: 3 × 3.2 = 9.6 → 10
Tan: 4 × 3.2 = 12.8 → 13

Same result. And 38+3+10+13=64. Good.

So for Part B:

White = 38
Blue = 3
Black = 10
Tan = 13

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Part C: How many PAIRS of each sock?

Since 1 pair = 2 socks, divide each by 2.

White: 38 ÷ 2 = 19 pairs
Blue: 3 ÷ 2 = 1.5 pairs → Uh oh! Can’t have half a pair. That’s a problem.

Wait — this suggests our prediction might be slightly off because we rounded.

Original unrounded:

White: 38.4 → 19.2 pairs
Blue: 3.2 → 1.6 pairs
Black: 9.6 → 4.8 pairs
Tan: 12.8 → 6.4 pairs

Still not whole numbers.

But the problem says “based on your results” — meaning based on the sample — so we should report the predicted number of pairs even if fractional? Or round to nearest whole pair?

Looking ahead to Part D, they give actual values: 16 white pairs, 2 blue, 6 black, 8 tan — which are all whole numbers.

Also, note: in Part D, it says “8 pairs of white socks” — but earlier it said “16 pairs of white socks” — that must be a typo! Wait, let me read again:

> D. Your drawer actually contains 16 pairs of white socks, 2 pairs of blue socks, 6 pairs of black socks, and 8 pairs of white socks.

That says “white socks” twice! Probably a mistake. Likely meant: 16 white, 2 blue, 6 black, 8 tan? Because 16+2+6+8=32 pairs — matches total.

Yes, that makes sense. So probably typo: last one should be “tan”.

Assuming that, actual:

White: 16 pairs → 32 socks
Blue: 2 pairs → 4 socks
Black: 6 pairs → 12 socks
Tan: 8 pairs → 16 socks
Total: 32+4+12+16=64 socks ✔

Back to Part C: We predicted:

Individual socks: White 38, Blue 3, Black 10, Tan 13

Pairs: White 19, Blue 1.5, Black 5, Tan 6.5

But since you can’t have half pairs, maybe we should adjust to make sense.

Perhaps the question expects us to report the decimal or rounded version? But in context, since it’s a prediction, maybe we leave as is? Or round to nearest whole pair?

Let’s see what makes sense with the sample.

In sample of 20 socks, we had:

White: 12 → 60%
Blue: 1 → 5%
Black: 3 → 15%
Tan: 4 → 20%

Apply to 32 pairs (since 32 pairs total):

White pairs: 60% of 32 = 0.6 × 32 = 19.2 → ~19
Blue: 5% of 32 = 1.6 → ~2
Black: 15% of 32 = 4.8 → ~5
Tan: 20% of 32 = 6.4 → ~6

Sum: 19+2+5+6=32 ✔

And these are whole numbers! Better.

How did I get that? Instead of applying to 64 socks, apply to 32 pairs directly using percentages from sample.

Sample: 20 socks → but since each sock is independent, the proportion of colors should be same whether we think in socks or pairs.

Proportion of white socks in sample: 12/20 = 0.6 → so 60% of all socks are white → so 60% of 32 pairs = 19.2 pairs → round to 19

Similarly:

Blue: 1/20 = 0.05 → 5% of 32 = 1.6 → round to 2
Black: 3/20 = 0.15 → 15% of 32 = 4.8 → round to 5
Tan: 4/20 = 0.2 → 20% of 32 = 6.4 → round to 6

Sum: 19+2+5+6=32 ✔

This gives whole numbers and adds up.

Moreover, in Part D, actual is 16 white, 2 blue, 6 black, 8 tan — so our prediction of 19,2,5,6 is close.

Whereas if we used 38 socks white → 19 pairs, etc., we had blue 1.5 which is messy.

So probably the intended way is to calculate predicted pairs directly from sample proportions applied to 32 pairs.

Let me confirm with the problem statement:

“you randomly pick 20 individual socks and predict the number from your results.”

It doesn’t specify whether to predict individual socks or pairs first, but since the final answer is asked in pairs in Part C, and total pairs is given (32), it makes sense to predict pairs directly.

So for Part C:

Predicted pairs:

White: (12/20)*32 = (3/5)*32 = 96/5 = 19.2 → 19
Blue: (1/20)*32 = 32/20 = 1.6 → 2
Black: (3/20)*32 = 96/20 = 4.8 → 5
Tan: (4/20)*32 = 128/20 = 6.4 → 6

Rounded to nearest whole number, and sum to 32.

Perfect.

So Part C:

White = 19
Blue = 2
Black = 5
Tan = 6

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Part D: Compare to actual

Actual (assuming typo corrected: 16 white, 2 blue, 6 black, 8 tan pairs)

Our prediction: 19 white, 2 blue, 5 black, 6 tan

Compare:

- White: predicted 19, actual 16 → overpredicted by 3
- Blue: predicted 2, actual 2 → exact!
- Black: predicted 5, actual 6 → underpredicted by 1
- Tan: predicted 6, actual 8 → underpredicted by 2

Overall, pretty close! Blue was perfect, others were off by 1-3 pairs.

To measure accuracy, we could calculate error per color or overall.

But the question just asks “how accurate was your prediction?” — so we can describe it.

Since it's a small sample (20 out of 64 socks), getting within 1-3 pairs is reasonable.

Note: Actual distribution:

White: 16/32 = 50%
Blue: 2/32 = 6.25%
Black: 6/32 = 18.75%
Tan: 8/32 = 25%

Our sample:

White: 12/20 = 60%
Blue: 5%
Black: 15%
Tan: 20%

So sample overestimated white, underestimated tan and black slightly, blue was close.

Prediction reflected the sample, so it's as accurate as the sample allows.

Answer for D: The prediction was fairly accurate. Blue was exact, white was a bit high, black and tan were a bit low. Given the small sample size, it's a good estimate.

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Now, let’s write the answers clearly.

Final Answers:

A.
P(white) = 3/5
P(blue) = 1/20
P(black) = 3/20
P(tan) = 1/5

B.
White = 38
Blue = 3
Black = 10
Tan = 13
*(individual socks)*

C.
White = 19
Blue = 2
Black = 5
Tan = 6
*(pairs)*

D.
The prediction was reasonably accurate. Blue matched exactly. White was overpredicted by 3 pairs, black underpredicted by 1, tan underpredicted by 2. Overall, close given the small sample.

But for Final Answer section, we need to box the numerical answers as per format.

Looking back at the worksheet, for A,B,C,D, they have blanks.

So for Final Answer, we should provide:

A. P(white)=3/5, P(blue)=1/20, P(black)=3/20, P(tan)=1/5

B. White=38, Blue=3, Black=10, Tan=13

C. White=19, Blue=2, Black=5, Tan=6

D. Description — but since it's text, perhaps summarize.

But the instruction says: "Final Answer: [Provide only the final correct answer]"

Probably for multiple parts, list them.

Since it's a worksheet, likely expect the filled blanks.

So I'll compile:

Final Answer:

A. P(white) = \frac{3}{5}, P(blue) = \frac{1}{20}, P(black) = \frac{3}{20}, P(tan) = \frac{1}{5}

B. White = 38, Blue = 3, Black = 10, Tan = 13

C. White = 19, Blue = 2, Black = 5, Tan = 6

D. The prediction was fairly accurate; blue was exact, white was overestimated by 3 pairs, black underestimated by 1 pair, tan underestimated by 2 pairs.

But to match format, perhaps just the numbers.

Since the user didn't specify, I'll provide concise final answers for each part.

Note: In Part B, some might argue to use the unrounded values, but since we need whole socks and they sum to 64 with rounding, 38,3,10,13 is fine.

Similarly for C, 19,2,5,6 sums to 32.

Okay.

Final Answer:

A. P(white) = 3/5, P(blue) = 1/20, P(black) = 3/20, P(tan) = 1/5
B. White = 38, Blue = 3, Black = 10, Tan = 13
C. White = 19, Blue = 2, Black = 5, Tan = 6
D. Prediction was close: blue exact, white +3, black -1, tan -2 pairs compared to actual (16,2,6,8).