NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
← Back to practice

Probability experiments and simulations

Wide tables scroll horizontally. For detailed working, you may prefer a larger screen.

Required skills (click to reveal)

In a sports equipment allocation simulation conducted in Sydney, a coach is distributing 69 basketballs and 57 footballs to two teams using a chance experiment. The coach conducts a two-step experiment: first, a ball is randomly selected from the combined pool of 126 balls (69 basketballs and 57 footballs) and removed without replacement; second, another ball is selected from the remaining 125.

What is the exact probability that both selected balls are basketballs? Express your answer as a simplified fraction.

Concept illustrations

These are separate worked examples of related concepts, not a diagram of this question. Their values and dimensions do not describe your question.

A fair-coin simulation model. Choose 0 or 1 with equal probability: 0 means tails and 1 means heads. Repeat independent trials and count outcomes. No experiment results are asserted here.Choose 0 or 1Equal chance→0=T 1=HMap outcome→RepeatCount heads
Choose 0 or 1 with equal probability: 0 means tails and 1 means heads. Repeat independent trials and count outcomes. No experiment results are asserted here.

Press Start when ready. Time includes time spent in another tab. Submit your answer before opening a help panel for a timed rank.

00:00
0 wordsOnly your numerical final answer or selected MCQ option is checked. Scratch working is not graded.

Report a problem or suggest an improvement

My notes — optional, not graded 0 words

Notes and scratch working stay in this browser and are linked to this question version. They are not graded or included in feedback. On shared devices, other people using this browser may see them.

For this question only. Your full notebook is on the dashboard.

Notes save in this browser. Download a copy to keep them elsewhere.

Report a problem or suggest an improvement

Your observations help improve this question. You can report an issue or recommend a better explanation, visual or experience.

0 words

The report includes your message and question/version details. Saved profile details, answers, notes and attempt history are not automatically attached. Leave out names and contact details, and check screenshots for personal information and embedded metadata.

Attachments may contain personal information. Review them before sharing. Logs collect only event codes and timestamps after you enable them. Download the ZIP to keep a copy, then attach it to an email if you choose.

Formula and explanation (click to reveal)

Opening this before your first submission makes the attempt practice only.

Formula

Explanation

Worked solution and answer (click to reveal)

Opening this before your first submission makes the attempt practice only.

Worked solution

  1. The total number of balls is 69 basketballs + 57 footballs = 126 balls.
  2. The first ball is selected at random from 126 balls. The probability it is a basketball is 69/126.
  3. After removing one basketball, 68 basketballs and 57 footballs remain, for a total of 125 balls.
  4. The probability the second ball is a basketball, given the first was a basketball, is 68/125.
  5. The probability of both events occurring (both basketballs) is the product of the two probabilities: (69/126) × (68/125).
  6. Multiply numerators: 69 × 68 = 4692.
  7. Multiply denominators: 126 × 125 = 15750.
  8. The combined fraction is 4692 / 15750.
  9. Simplify the fraction by finding the greatest common divisor (GCD) of 4692 and 15750. First, factor both numbers.
  10. GCD(4692, 15750) = 6. Divide numerator and denominator by 6: 4692 ÷ 6 = 782, 15750 ÷ 6 = 2625.
  11. The simplified fraction is 782 / 2625. Check that 782 and 2625 have no common factors (782 = 2×17×23, 2625 = 3×5^3×7).
  12. Therefore, the exact probability that both selected balls are basketballs is 782/2625.

Reference answer: 782/2625

Alternative methods (click to reveal)

Shortcuts are shown only when applicable. Check the conditions before using one.

Earlier attempts for this question

#Date / timeYour answerResultSecondsHelp revealedRank
History stays in this browser when storage is available. Export it to your shared Drive folder and import it on another computer.
Worksheet details

Naming pattern: Topic_Grade_Complexity_YYYYMMDD_HH24MISS.html

Validation compares your answer with the generated reference. The model's reference can be wrong. Time ranks use an estimated student solving time, not a measured benchmark or a comparison with other students. An incorrect answer receives no speed rank.

NavGanitMate privacy & saved work

Saved in this browser. Your profile preferences, answers, practice history and notes are stored here when browser storage is available. They are not automatically uploaded to our servers. People sharing this browser may see saved work; changing the learner name does not create a separate private account. A nickname is enough.

Keep copies of important work. Clearing browser data, private browsing or changing browser or device can mean losing saved work. Download notes and export history separately. Downloads are copies of the selected content, not a complete account backup; not every format can be imported to restore your work. Keep these files somewhere private.

Visiting the website. Cloudflare helps deliver and protect this site and processes connection information such as IP addresses and requested pages. Server error logs may also contain request details. Security features may use cookies. This is separate from your browser-saved learning records. Cloudflare privacy information.

A parent-connection reminder uses a local list of up to five completed question IDs for this browser profile and a tab-session dismissal marker. Reminder activity is not uploaded and practice remains available.

Sharing feedback is your choice. A report includes your message and question/version details. Your saved profile, answers and notes are not automatically attached. Files you select can reveal personal details or contain embedded metadata: check and redact them before sharing. Diagnostic event codes and timestamps are included only after you enable logging. Sending email shares your message and attachments with the recipient and email providers. A download alone sends nothing to us. Website feedback delivery may be unavailable; only a confirmed receipt indicates it was received.