Unit 4 · Statistics and Probability
Marble Box — Find the Least Likely Colour
Lesson 2 of 6
25 marbles: 3 blue, 4 red, 8 yellow, 10 green. Which event is least likely? Count favourable outcomes for each: A=7, B=8, C=15, D=22, E=11. Smallest = 7 = Option A. The key skill: for 'not X' and 'neither X nor Y' events, subtract from the total.
Comparing probabilities by counting favourable outcomes is an easy-level staple in OC MR. The twist here — 'not X' and 'neither X nor Y' options — tests whether students can compute complementary event counts by subtracting from the total.
The examiner tests whether students can translate compound events ('either/or', 'not', 'neither/nor') into counts, then rank them. Option B (yellow, 8) is the classic distractor — students who stop at 'yellow is the rarest single colour' miss that blue+red combined (7) is actually fewer.
A bag or box contains coloured objects with given counts. One is drawn at random. Students evaluate several events (including compound 'not' and 'neither/nor' events) and identify the least or most likely.
Best approach: Convert every event to a count: A=3+4=7, B=8, C=25−10=15, D=25−3=22, E=25−4−10=11. Rank: 7<8<11<15<22. Least likely = A.
Question
A box contains 25 marbles:
3 blue, 4 red, 8 yellow and 10 green.
Lemar takes one marble out of the box without looking.
Which of these events is the least likely?
Select an answer to see the explanation.
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