Proportionality>Solving Problems with Predictions and Comparisons from Experiments(TEKS.Math.7.6.H)
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Texas 7th Grade Math › Proportionality>Solving Problems with Predictions and Comparisons from Experiments(TEKS.Math.7.6.H)
A coin was flipped 20 times and landed on heads 13 times and tails 7 times. Predict results for 100 trials.
About 65 heads and 35 tails
About 50 heads and 50 tails
About 70 heads and 30 tails
About 13 heads and 7 tails
Explanation
Use the experimental proportion. Heads were $13/20=0.65$, so in 100 flips expect about $0.65\times 100=65$ heads and $35$ tails. The theoretical probability is $1/2$ each, but experimental results can vary due to randomness.
A spinner with 4 equal sections (A, B, C, D) was spun 60 times: A appeared 15 times, B 10 times, C 22 times, and D 13 times. Predict results for 100 trials: How many times should it land on C?
About 25
About 37
About 22
About 50
Explanation
Experimental proportion for C is $22/60\approx 0.367$. Scaling to 100 spins gives about $0.367\times 100\approx 37$. Theoretical probability is $1/4=0.25$, but experiments often differ due to variability.
A number cube was rolled 40 times with these outcomes: 1: 4 times, 2: 9 times, 3: 7 times, 4: 6 times, 5: 8 times, 6: 6 times. How does the experimental probability of rolling an even number compare to the theoretical probability?
It is much lower than the theoretical 1/2.
It is exactly equal to the theoretical 1/2.
It is slightly greater than the theoretical 1/2.
It is much greater than the theoretical 1/2.
Explanation
Even outcomes (2, 4, 6) occurred $9+6+6=21$ times out of $40$, so $21/40=0.525$, which is slightly above the theoretical $1/2=0.5$. Small differences are expected from experimental variability.
A bag of marbles was sampled with replacement 80 times: red 36, blue 24, green 20. Predict results for 100 trials: How many blue draws are expected?
About 33
About 24
About 20
About 30
Explanation
Blue occurred $24/80=0.30$ of the time. Scaling to 100 trials gives $0.30\times 100=30$. The exact theoretical probability depends on the true bag composition; experiments can differ due to randomness.
A spinner with 3 equal sections (X, Y, Z) was tested 90 times: X appeared 20 times, Y 35 times, Z 35 times. How does the experimental probability for X compare to the theoretical probability?
It matches the theoretical 1/3 exactly.
It is less than the theoretical 1/3.
It is greater than the theoretical 1/3.
It cannot be compared to the theoretical probability.
Explanation
Experimental probability for X is $20/90\approx 0.222$, while the theoretical probability is $1/3\approx 0.333$. So the experimental result is lower. Differences are normal in finite trials.