Two Events – Use of Sample Spaces (Leaving Cert Mathematics): Flashcards

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Two Events – Use of Sample Spaces
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Definition of sample space

Complete collection of all possible outcomes in an experiment

Sample space for two coins

{HH, HT, TH, TT}

Probability formula using sample space

favorable outcomestotal outcomes\frac{\text{favorable outcomes}}{\text{total outcomes}}

Purpose of sample space tables

Organise outcomes systematically for complex experiments

Product rule for independent events

Total outcomes = product of individual outcomes

Outcomes for coin and die together

12 (2 × 6)

Total outcomes when throwing two dice

36 (6 × 6)

P(sum=7)P(sum = 7) with two dice

16\frac{1}{6} or 636\frac{6}{36}

Ways to get sum of 7 with two dice

6 ways: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)

P(sum≤4)P(sum \leq 4) with two dice

16\frac{1}{6} or 636\frac{6}{36}

P(sum≥11)P(sum \geq 11) with two dice

112\frac{1}{12} or 336\frac{3}{36}

How to express probability answers

Always simplify fractions to simplest form

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