This document discusses key concepts in probability, including experiments, sample spaces, events, and calculating probabilities. It provides examples of identifying the sample space for different experiments like flipping a coin or rolling a die. Events are defined as subsets of the sample space, and probability is calculated as the number of outcomes in the event divided by the total number of outcomes in the sample space. Mutually exclusive events and unions and intersections of events are also introduced.

1. PROBABILITY
Grade 10

2. ◦ Any activity with an unpredictable results is
called an EXPERIMENT.
◦ The results of an experiment are called
OUTCOMES and the set of all possible outcomes
is the SAMPLE SPACE.
◦ Examples: Identify the sample space.
◦ Experiment Sample space n(S)
◦ Flip a coin. S = {H, T} 2
◦ Toss a die. S = {1, 2, 3, 4, 5, 6} 6

3. Coin: Heads and tails

4. Cards

5. ◦ Any subset of the sample space is called an EVENT.
◦ The number of outcomes in an event E is n(E).
◦ Examples: List the outcomes in each event.
◦ EXPERIMENT EVENT n(E)
◦ Toss a die Get heads {H} 1
◦ Toss a die Draw a card Get an even number {2, 4, 6} 3
◦ Flip two coins Get a 3 or higher {3, 4, 5, 6} 4
◦ Draw a card Get an 8 { 8, 8, 8, 8} 4

6. If E is an event from a sample space S of equally likely
outcomes, the PROBABILITY of event E is: P(E)= n(E)/n(S)
Note that 0 < P(E) <1.
◦ If n(E) = 0, then P(E) = 0, and the event is IMPOSSIBLE.
◦ If n(E) = n(S), then P(E) = 1 and the event is CERTAIN.
◦ Examples: A 6-sided die is rolled once

7. What is the probability?
◦P(10) = 0/10 =0 the event is
impossible
◦P(n<10) = 6/6 =1 the event is certain
◦P(5)= 1/6

8. Example 1: Two coins are tossed.
What is the probability that at least one head comes up?
S = {HH, HT, TH, TT} E = {HH, HT, TH}

9. Probability
◦ P(E) = n(E)/n(S) =3/4
◦ Example 2: A card is drawn at random from a standard deck of 52 cards.
What is the probability the card drawn is a face card?
◦ S = all 52 cards in the deck
◦ n(S) = 52 E
◦ = { J, J, J, J, Q, Q, Q, Q, K, K, K, K}
◦ n(E) = 12

10. Two events A and B are MUTUALLY EXCLUSIVE if they have no
outcomes in common, A and B = mutually exclusive.
Example: When a die is tossed, which events are mutually exclusive?
A: getting an even number B: getting an odd number C: getting 5 or 6.
◦A: getting an even number B: getting
an odd number C: getting 5 or 6.
◦Venn diagram is the best way to
represent this. Let us represent this
using a venn diagram

11. Venn diagram

12. Union events
◦ If A and B are events, their UNION, written A or B
◦ consisting of all outcomes in A or in B or in both A and B. A B = { J, J,
J, J, Q, K }
◦ Example: A card is drawn at random from a standard deck of 52 cards.
◦ A: getting a club face card B: getting a jack
◦ Use a venn diagram to express this
◦ List the outcomes for the event of getting a club face card or getting a jack

13. Intersection
◦ If A and B are events, their INTERSECTION, written A and B, is the
◦ event “A and B” consisting of all outcomes common to both A and B.
◦ Example: A card is drawn at random from a standard deck of 52 cards.
◦ A: getting a club face card B: getting a jack.
◦ Draw venn diagram
◦ List the outcomes for the event of getting a club face card and getting a
jack.

14. Take a short break…we will continue later