Use this as an opportunity for practical work. Probabilities written in fraction form should be cancelled to their simplest form. 13b. Probability II Teaching time (N5, P1, P2, P3, P5, P7, P8) 8–10 hours OBJECTIVES By the end of the sub-unit, students should be able to: Find the probability of an event happening using relative frequency; Estimate the number of times an event will occur, given the probability and the number of trials – for both experimental and theoretical probabilities; List all outcomes for combined events systematically; Use and draw sample space diagrams; Work out probabilities from Venn diagrams to represent real-life situations and also ‘abstract’ sets of numbers/values; Use union and intersection notation; Compare experimental data and theoretical probabilities; Compare relative frequencies from samples of different sizes; Find the probability of successive events, such as several throws of a single dice; Use tree diagrams to calculate the probability of two independent events; Use tree diagrams to calculate the probability of two dependent events. POSSIBLE SUCCESS CRITERIA Understand the use of the 0–1 scale to measure probability. List all the outcomes for an experiment. Know and apply the fact that the sum of probabilities for all outcomes is 1. Draw a Venn diagram of students studying French, German or both, and then calculate the probability that a student studies French given that they also study German. COMMON MISCONCEPTIONS Not using fractions or decimals when working with probability trees. NOTES Probability without replacement is best illustrated visually and by initially working out probability ‘with’ replacement. Encourage students to work ‘across’ the branches working out the probability of each successive event. The probability of the combinations of outcomes should = 1. Emphasise that were an experiment repeated it will usually lead to different outcomes, and that increasing sample size generally leads to better estimates of probability and population characteristics. Probabilities written in fraction form should be cancelled to their simplest form.
Use this as an opportunity for practical work. Probabilities written in fraction form should be cancelled to their simplest form. 13b. Probability II (N5, P1, P2, P3, P5, P7, P8) Teaching time 8–10 hours OBJECTIVES By the end of the sub-unit, students should be able to: Find the probability of an event happening using relative frequency; Estimate the number of times an event will occur, given the probability and the number of trials – for both experimental and theoretical probabilities; List all outcomes for combined events systematically; Use and draw sample space diagrams; Work out probabilities from Venn diagrams to represent real-life situations and also ‘abstract’ sets of numbers/values; Use union and intersection notation; Compare experimental data and theoretical probabilities; Compare relative frequencies from samples of different sizes; Find the probability of successive events, such as several throws of a single dice; Use tree diagrams to calculate the probability of two independent events; Use tree diagrams to calculate the probability of two dependent events. POSSIBLE SUCCESS CRITERIA Understand the use of the 0–1 scale to measure probability. List all the outcomes for an experiment. Know and apply the fact that the sum of probabilities for all outcomes is 1. Draw a Venn diagram of students studying French, German or both, and then calculate the probability that a student studies French given that they also study German. COMMON MISCONCEPTIONS Not using fractions or decimals when working with probability trees. NOTES Probability without replacement is best illustrated visually and by initially working out probability ‘with’ replacement. Encourage students to work ‘across’ the branches working out the probability of each successive event. The probability of the combinations of outcomes should = 1. Emphasise that were an experiment repeated it will usually lead to different outcomes, and that increasing sample size generally leads to better estimates of probability and population characteristics. Probabilities written in fraction form should be cancelled to their simplest form.
GCSE%20(9-1)%20Mathematics%20Edexcel%203-year%20Scheme%20of%20Work%20Issue%202.docx