Making Predictions with Data

Project-based Learning; Talk for Learning, Think-pair-share, Experiential Learning; and Group Work/Collaborative Learning.
Learning Experience: Learners work in mixed-ability gender groups, to solve binomial probability problems.
Activity 1: Binomial probability Learners think pair and share ideas on situations or events involving likelihood of combining or selecting or succeeding in one out of two outcomes in a certain number of attempts and use the idea to solve binomial probability problems. E.g. The probability of passing 2 times in a semester examination in Add Mathematics after attempting 5 times.
Definition: Binomial probability refers to the probability of exactly 𝒙 successes on 𝒏 repeated trials in an experiment which has two possible outcomes.
Activity 2: The idea of combination in binomial probability Learners in mixed-ability groups solve real life problems on combination and discuss how combination relates to the binomial probability.
Example 1: A group of 4 SRC executives is to be selected from 5 males and 6 females of the SRC. Find the number of ways of selecting the group if:
- There are no restrictions on its composition
- There is an equal number of males and females
- It consists of all males or all females.
Solution: !!! !!×!(×2×1 11𝐶 , = = = 330 𝑤 ,!7! ,×"×)
5𝐶 ) × 6𝐶 ) = 10 × 15 = 150 𝑤
5𝐶 ) + 6𝐶 ) = 10 × 15 = 25 𝑤
Activity 3: Solving real life problems on binomial probability Learners use Talk for Learning strategy to describe the probability P that an event will happen in any single trial (success) and the probability that the event will fail to happen (failure) after a given number of attempts. Mathematically, the probability that an event will happen "x" times in 'n' trials is given by 𝑃(𝑋 = 𝑥) = 𝑛𝐶 0 𝑝 0 𝑞 %*0 where
𝑛 = 𝑛 𝑜 𝑡 𝑝 = 𝑝 𝑜 𝑠 𝑞 = 𝑝 𝑜 𝑓 Note:
- p + q = 1
- Success is what we are interested in
- Failure is what we are not interested in.
Solution: 𝑛 = 6 3 1 𝑝 = 𝑝(𝑑) = = 12 4
1 𝑞 = 𝑞(𝑛 − 𝑑) = 1 − 4
! ! " . /
- 𝑃(𝑥 = 1) = i ( j i , j i , j
! )," =6× × = 0.355957 = 0.356 , !(),
- 𝑃(𝑥 ≤ 1) = 𝑃 (𝑥 = 0) + 𝑃(𝑥 = 1) ! ( " / / = i ( j i , j i , j + 𝑃(𝑥 = 1) 729 = + 0.355957 4096 = 0.1779785 + 0.355957 = 0.534
Example 2: A student tosses a fair coin 5 times. Find the probability that there will be:
- Exactly 3 tails
- At least 1 head.
Solution:
𝑛 = 5 1 1 𝑝 = , 𝑞 = 2 2 ! " ! ) ! ! !( . 𝑃(𝑥 = 3) = 5𝐶 " i j i j =10 × × = = ) ) 1 , ") !/
ii) 𝑃(𝑎 𝑙 𝑜 ℎ𝑒) = 𝑃(𝑋 ≥ 1) 𝑃(𝑋 ≥ 1) = 1 − 𝑃(𝑋 = 0) 1 ( 1 . = 1 − (5 0 ) £ ¤ £ ¤ 2 5 1 =1− 32 31 = 32
Activity 3: Modelling real life problems on binomial probability Learners in groups create more real life examples of binomial distribution and calculate the probabilities.
Teaching and Learning Resources:
- SHS curriculum calculators
Assessment (3.4.2.AS.4). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning.