Probabilities from experiments and statistical displays

Use experimental results and statistical displays to estimate probabilities.

All objectives

Foundation

16 web questions

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  1. A coin is tossed $20$ times and lands heads $11$ times. Estimate the probability of heads.
  2. A die is rolled $30$ times and a $6$ appears $4$ times. Estimate the probability of rolling a $6$.
  3. A spinner lands on red $9$ times in $15$ spins. Estimate the probability of red.
  4. In $25$ draws from a bag, a blue counter is picked $10$ times. Estimate the probability of blue.
  5. A survey chart shows $18$ of $30$ students walk to school. Estimate the probability that a randomly chosen student walks to school.
  6. A weather record shows rain on $6$ of the last $10$ days. Estimate the probability of rain tomorrow using this data.
  7. A coin lands tails $14$ times in $20$ tosses. Write the experimental probability of tails.
  8. A spinner lands on green $7$ times in $28$ spins. Write the experimental probability of green.
  9. Out of $40$ penalty shots, $26$ are scored. Estimate the probability of scoring.
  10. Out of $50$ seeds planted, $35$ sprout. Estimate the probability that a seed sprouts.
  11. Which is greater: an experimental probability of $\frac{9}{20}$ or $\frac{1}{2}$?
  12. Which is smaller: $30\%$ success or $\frac{2}{5}$ success?
  13. Fill in the blank: $12$ wins from $20$ games gives an experimental probability of $\frac{\square}{20}$.
  14. Fill in the blank: $15$ successes from $25$ trials gives an experimental probability of $\square\%$.
  15. A student says $3$ reds in $12$ draws means the probability of red is $\frac{1}{3}$. Are they correct?
  16. Explain in one short sentence what experimental probability means.

Proficient

10 web questions

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  1. A coin is tossed $80$ times and lands heads $37$ times. Estimate the probability of heads as a fraction and decimal.
  2. A die is rolled $60$ times and an even number appears $34$ times. Estimate the probability of rolling an even number.
  3. A spinner lands on blue $18$ times in $45$ spins. Estimate the probability of blue.
  4. A bus is late on $9$ of the last $24$ school days. Estimate the probability it is late on a future school day.
  5. In a tally chart, $14$ of $35$ customers choose mango. Estimate the probability that the next customer chooses mango.
  6. A class bar chart shows $12$ students play football, $9$ netball, $6$ basketball, and $3$ hockey. Estimate the probability a randomly chosen student plays netball.
  7. A bag is sampled $50$ times with replacement and a yellow counter appears $21$ times. Estimate the probability of yellow.
  8. In $120$ free throws, a player scores $78$. Estimate the probability of scoring a free throw.
  9. Which is closer to $\frac{1}{2}$: $24$ successes in $50$ trials or $17$ successes in $30$ trials?
  10. Fill in the blank: $48$ correct answers from $60$ questions gives an experimental probability of $\square\%$.

Excellence

10 web questions

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  1. A student says $41$ heads in $80$ tosses proves a coin is unfair. Are they correct? Explain.
  2. A spinner has four equal sectors, so the theoretical probability of red is $\frac{1}{4}$. In $12$ spins red appears $6$ times. Compare the experimental and theoretical probabilities.
  3. A bar chart shows bus arrivals over $50$ days: early $8$, on time $29$, late $13$. Estimate the probability that tomorrow's bus is late.
  4. A survey of $120$ students shows $54$ bring lunch, $42$ buy lunch, and $24$ go home. Estimate the probability a randomly chosen student buys lunch.
  5. A basketball player scores $63$ shots from $90$ attempts. Estimate the probability of scoring, as a fraction in simplest form and as a percentage.
  6. In a science test, $18$ of $30$ seedlings survive in one tray and $52$ of $80$ survive in another. Which tray has the higher survival probability?
  7. A machine makes faulty items with theoretical probability $0.08$. In a sample of $150$ items, $18$ are faulty. Is the experimental probability above or below the theoretical probability?
  8. A coin is tossed $200$ times and lands heads $94$ times. Is this result closer to $0.45$, $0.47$, or $0.50$? Explain.
  9. Which is greater: $17$ wins from $40$ games or $31$ wins from $70$ games? Show enough working to justify.
  10. A hospital record shows $126$ of $300$ patients waited under $15$ minutes. Estimate the probability that the next patient waits under $15$ minutes.