Grade 10 · Core Mathematics · Lesson 5 of 12

Generating Probability Space for Compound Events

A Grade 10 Core Mathematics CBE lesson from the sub-strand Probability 1. In it, learners list all possible outcomes when tossing two or three coins simultaneously.

Strand Statistics and ProbabilitySub-strand Probability 1Lesson code 10CM-32-L540 minutes · 3 slides

KICD learning outcome (c)

Generate probability space of different events.

By the end of this lesson, learners should be able to

List all possible outcomes when tossing two or three coins simultaneously.
Construct and interpret outcome space tables for combined experiments involving a six-sided die with a coin.
Generate probability spaces for sums and products of two dice using grids and tree diagrams.

Key vocabulary

Probability space: The set of all possible outcomes resulting from a random statistical experiment.; The probability space for rolling a six-sided die contains six distinct numerical outcomes.
Compound event: An event formed by combining two or more simple probability outcomes together.; Getting a Head on a coin and a six on a die is a compound event.

Lesson preview

Slide 1 · Sample Space of Coin ExperimentsOpening · 12 min

Figure 1: A tree diagram mapping out the eight possible outcomes when tossing a coin three times, from three heads to three tails.

When multiple coins are thrown simultaneously, the set of all possible outcomes forms a probability space. For two coins, each outcome is written as a pair such as $(H, T)$ , giving a sample space of size $4$ . Tossing three coins expands the sample space systematically to $8$ outcomes, from $(H, H, H)$ to $(T, T, T)$ . Listing every combination ensures no possible outcome is omitted when calculating probabilities.

Tossing two fair coins yields four distinct combined outcomes in the probability space: HH, HT, TH, and TT.
The sample space size for tossed coins follows a power of two pattern: $2^{n}$ for $n$ coins.
When tossing three coins, systematic listing produces eight total outcomes from HHH to TTT without omission.
Listing all possible outcomes allows learners to analyse coin events and calculate theoretical probabilities accurately.

Worked example. For each coin, the outcome is either Head (H) or Tail (T). Write outcomes systematically: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. Count the total number of listed outcomes:

2^{3} = 8

. Answer: ${H H H, H H T, H T H, H T T, T H H, T H T, T T H, T T T}$ , total = 8.

Check question: If 3 fair coins are thrown simultaneously, what is the probability of obtaining at least two Heads?

$\frac{1}{8}$
$\frac{3}{8}$
$\frac{1}{2}$
$\frac{7}{8}$

Show answer

$\frac{1}{2}$ . When 3 coins are thrown, the total number of possible outcomes is $2^{3} = 8$ . The complete sample space is ${H H H, H H T, H T H, H T T, T H H, T H T, T T H, T T T}$ . The outcomes with at least two Heads are HHH, HHT, HTH, and THH. Since there are 4 favourable outcomes out of 8, the probability is $P = \frac{4}{8} = \frac{1}{2}$ .

Slide 2 · Outcome Space Tables for Combined EventsModel · 14 min

Figure 2: A table displaying the twelve possible outcomes of tossing a coin and rolling a six-sided die.

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All 3 slides with diagrams and class activities
Teacher notes, SNE adaptations and assessment checks
Homework and the other 11 lessons in this sub-strand

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Generating Probability Space for Compound Events

By the end of this lesson, learners should be able to

Key vocabulary

Lesson preview

Teach the full lesson on the projector

All 12 lessons in Probability 1