Proportionality>Using Simulations to Represent Simple and Compound Events(TEKS.Math.7.6.B)
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Texas 7th Grade Math › Proportionality>Using Simulations to Represent Simple and Compound Events(TEKS.Math.7.6.B)
A basketball player makes a free throw about 70% of the time. You want to simulate one free throw. Which simulation best models this?
Flip a fair coin; heads = made, tails = missed.
Roll a fair number cube; 1–4 = made, 5–6 = missed.
Spin an 8-section spinner; 6 shaded = made, 2 unshaded = missed.
Use random digits 0–9; 0–6 = made, 7–9 = missed.
Explanation
Using digits 0–9 gives 10 equally likely outcomes, and marking 7 of them as made matches $7/10 = 70%$. The others model $1/2$, $4/6$, or $6/8$, which are $50%$, about $66.7%$, and $75%$, not $70%$.
The forecast says there is a 30% chance of rain each day, and days are independent. You want to simulate the weather for a 5-day week. Which simulation best models this?
Roll a fair number cube once per day; rain if 1 or 2, no rain otherwise. Do this for 5 days.
Use random digits 0–9 once per day; rain if the digit is 0, 1, or 2, no rain otherwise. Do this for 5 days.
Spin a spinner with 8 equal sections once per day; rain if it lands on one of 3 shaded sections. Do this for 5 days.
Use a 00–99 table once per day; rain if the number is 00 through 30 (inclusive). Do this for 5 days.
Explanation
Digits 0–9 are 10 equally likely outcomes per day; choosing 0,1,2 as rain gives $3/10=30%$ and repeating 5 times models 5 independent days. The others give $2/6\approx33.3%$, $3/8=37.5%$, or $31/100=31%$.
A jar has 1 red marble and 3 blue marbles. You draw a marble, replace it, and draw again. Which simulation best models the two draws?
Roll a fair number cube twice; red if 1 or 2, blue otherwise.
Flip a fair coin twice; heads = red, tails = blue.
Spin a fair 4-section spinner with 1 section for red and 3 sections for blue; spin twice with replacement.
Use random digits 0–9 twice; red if the digit is 0 or 1, blue otherwise.
Explanation
With 1 red and 3 blue, the chance of red on each draw is $1/4$. A 4-section spinner with 1 red section and 3 blue sections, spun twice with replacement, matches this. The others model $2/6$, $1/2$, or $2/10$, not $1/4$.
For a website, a video loads in under 1 second 40% of the time. If it loads fast, the user clicks like 50% of the time. You want to simulate the event "fast load and like." Which simulation best models this?
For each visitor, use a random digit 0–9: 0–3 = fast, 4–9 = slow. If fast, flip a fair coin; heads = like. Count a success only when both happen.
Spin a 10-section spinner once per visitor; success if it lands on any of 5 shaded sections.
Roll a fair number cube once; 1–4 = fast, 5–6 = slow. If fast, roll again and count like only if a 1 appears.
Use one 00–99 number per visitor; success if it is 00–39 for fast and 00–49 for like, using the same number for both decisions.
Explanation
Fast corresponds to $4/10=40%$, and like is $1/2$. Using an independent coin flip after a fast load models the conditional step correctly. The others either model the wrong probability, use too-small like chance, or fail to keep the two steps independent.
You roll two fair number cubes and look at the sum. You want to simulate the event that the sum is 7. Which simulation best models this?
Spin a 12-section spinner once; success if it lands on the section labeled 7.
Flip three fair coins; success if exactly one head occurs.
Generate two random digits 0–9 and add them; success if the sum is 7.
Roll two fair number cubes and record a success if their sum is 7.
Explanation
Rolling two fair number cubes directly mirrors the real process and the non-uniform sum distribution (e.g., the six favorable pairs for 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)). The other methods do not produce the same outcome space or probabilities.