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

Sample spaces and probability

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

Required skills (click to reveal)

In a community garden in Melbourne, a rectangular plot is divided into 44 equal-sized sections for growing vegetables. Each section is assigned a unique number from 1 to 44.

A resident randomly selects one section to plant lettuce. What is the exact probability that the selected section number is a multiple of 4 or 6?

Express your answer as a simplified fraction. (Hint: Use inclusion-exclusion principle to count the number of favourable outcomes.)

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 sample is part of a population. The large outline represents a population of 24 members. Six filled members illustrate a sample. This picture does not establish that a selection process was random.6 selected from 24
The large outline represents a population of 24 members. Six filled members illustrate a sample. This picture does not establish that a selection process was random.
Median, mode and range in sorted data. The ordered values are 2,3,3,8,9. The middle value is 3, the most frequent value is 3, and the range is 9 − 2 = 7. The row uses equal spacing, not a number-line scale.23389↑ medianmode 3 range 7
The ordered values are 2,3,3,8,9. The middle value is 3, the most frequent value is 3, and the range is 9 − 2 = 7. The row uses equal spacing, not a number-line scale.

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 sections is 44, each uniquely numbered from 1 to 44. This is the sample space, so the total number of possible outcomes is 44.
  2. We need to find the number of sections where the number is a multiple of 4 or 6. This is a union of two sets: multiples of 4 and multiples of 6.
  3. Use the inclusion-exclusion principle: |A ∪ B| = |A| + |B| - |A ∩ B|, where A is multiples of 4, B is multiples of 6.
  4. Count the multiples of 4 from 1 to 44: 4, 8, 12, ..., 44. This is an arithmetic sequence with first term 4, last term 44, common difference 4. Number of terms = (44 - 4)/4 + 1 = 40/4 + 1 = 10 + 1 = 11.
  5. Count the multiples of 6 from 1 to 44: 6, 12, 18, ..., 42. First term 6, last term 42, common difference 6. Number of terms = (42 - 6)/6 + 1 = 36/6 + 1 = 6 + 1 = 7.
  6. Find the common multiples of 4 and 6, i.e., multiples of their LCM. LCM(4,6) = 12. So count multiples of 12: 12, 24, 36. First term 12, last term 36, common difference 12. Number of terms = (36 - 12)/12 + 1 = 24/12 + 1 = 2 + 1 = 3.
  7. Apply inclusion-exclusion: number of favourable outcomes = 11 (multiples of 4) + 7 (multiples of 6) - 3 (common multiples) = 15.
  8. The probability is the number of favourable outcomes divided by total outcomes: 15 / 44.
  9. Check if 15/44 can be simplified. GCD of 15 and 44 is 1, so the fraction is already in simplest form.
  10. The probability that the selected section number is a multiple of 4 or 6 is 15/44.
  11. Verify by listing: multiples of 4: 4,8,12,16,20,24,28,32,36,40,44 (11 numbers). Multiples of 6: 6,12,18,24,30,36,42 (7 numbers). Common: 12,24,36 (3 numbers). Union: 11 + 7 - 3 = 15. Correct.
  12. Final answer: 15/44.

Reference answer: 15/44

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.