Unit 12 · Multi-Step Conditional Reasoning

Lily & Tom — How Many Cards to Be Certain?

Lesson 15 of 16

Premium

About this lesson

Darren has a 15-card deck with 5 red, 5 blue, and 5 yellow cards numbered 1–5. Lily says drawing 11 cards guarantees all three colours; Tom says drawing 7 cards guarantees three different numbers. Are they right? This question introduces one of the most powerful reasoning patterns in OC TS: worst-case thinking. Instead of asking "what might happen?", you ask "what is the worst that can happen, and when does even that worst case guarantee the result?"

Chapters

0:00Introduction
0:21The Question
1:10Exam Strategy – The Worst-Case Scenario
1:37Testing Lily's Claim (Colours)
2:13Testing Tom's Claim (Numbers)
2:50Final Answer Selection

Question

| Darren has a deck of fifteen special playing cards:

  • Five red cards, numbered 1–5
  • Five blue cards, numbered 1–5
  • Five yellow cards, numbered 1–5
He shuffles the deck randomly, and then draws a number of cards from the top.

Lily: "To be certain of having all three colours, he has to draw eleven cards."

Tom: "To be certain of having three different numbers, he needs to draw seven cards."

If the information in the box is true, whose reasoning is correct?

Free account · OC

Take your OC prep further

  • Sample questions & worked solutions across core OC topics
  • Digital exam simulator with interactive practice sets
  • Personalised progress tracking across all your devices
Create free account

Already have an account? Log in here

No payment required. Compare OC plans

0 of 16 lessons completed

0%

Give Your Child the Best Chance at OC Entry

Join NSW families preparing their children for the Opportunity Class Placement Test with the most realistic online OC practice tests available. First tests free—no credit card required.

Claim Your Free OC Practice Tests