SHS3 Mathematics · Semester 2, Week 18
Probability/chance
Full lesson notes coming
Notes for this lesson are being prepared. The curriculum details below are complete and ready to use for your planning.
Curriculum details
- Strand
- Making Sense of and Using Data (Strand 4)
- Sub-strand
- Probability/chance (4.2)
- Content standard
- 3.4.2.CS.1 - Demonstrate an understanding of the role of probability in society and apply probability reasoning to analyse and make useful predictions about everyday life events. 3.4.2.LO.1 Explain how a given probability from print and electronic media influences individual decisions; select and analyse real-life data to solve problems involving the probability of two dependent and independent events.
- Indicator
- 3.4.2.LI.2 - Solve everyday life problems involving the probability of two dependent and independent events, including addition and multiplication laws.
- Suggested placement
-
Semester 2, Week 18
(Week 38 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
- Curriculum reference
- NaCCA curriculum document, p. 382
Exemplars (from the NaCCA curriculum)
Encourage learners to use their communication skills, combined problem-solving competencies and critical thinking skills to discuss and solve everyday life problems involving the probability of two dependent and independent events using addition and multiplication laws. Examples i. A card is chosen at random from a standard deck of 52 playing cards. Without replacing it, a second card is chosen. What is the probability that the first card chosen is a queen and the second card chosen is a jack? ii. Mr. Mills needs two students to help him with a science demonstration for his class of 15 girls and 13 boys. He randomly chooses one student who comes to the front of the room. He then chooses a second student from those still seated. (Note that the sample space of the dependent event will change.) What is the probability that both students chosen are girls? iii. In a shipment of 20 computers, 3 are defective. Three computers are randomly selected and tested. What is the probability that all three are defective if the first and second ones are not replaced after being tested? iv. A school has 200 seniors, of whom 140 will be going to college next year. Forty will be going directly to work. The remainder are taking a gap year. Fifty of the seniors going to college play sports. Thirty of the seniors going directly to work play sports. Five of the seniors taking a gap year play sports. What is the probability that a senior is taking a gap year? v. Studies show that about one woman in seven (approximately 14.3%) who live to be 90 will develop breast cancer. Suppose that of those women who develop breast cancer, a test is negative 2% of the time. Also, suppose that in the general population of women, the test for breast cancer is negative about 85% of the time. Let B = woman develops breast cancer and let N = tests negative. Suppose one woman is selected at random. a) What is the probability that the woman develops breast cancer? What is the probability that the woman tests negative? b) Given that the woman has breast cancer, what is the probability that she tests negative? c) What is the probability that the woman has breast cancer AND tests negative? d) What is the probability that the woman has breast cancer or tests negative? e) Are having breast cancer and testing negative independent events? f) Are having breast cancer and testing negative mutually exclusive? Teaching and Learning Resources: - Manipulative (dice, coins, spinners, playing cards, counters, digit cards) - Simple Probability Mazes (Printable & Digital) - Worksheets - Task Cards - Mathematical sets Assessment (3.4.2.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning.