Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
×
1 of 14

# Probability

3

Share

Learners should have a overall understanding of probability concepts and the big ideas such as indent events, mutually exclusive events, union, complementary events

See all

See all

### Probability

1. 1. PROBABILITY Grade 10
2. 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. 3. Coin: Heads and tails
4. 4. Cards
5. 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. 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. 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. 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. 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. 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. 11. Venn diagram
12. 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. 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. 14. Take a short break…we will continue later