PROBABILITY 2 and ANALYSIS OF DATA
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1 LO PROBABILITY 2 and ANALYSIS OF DATA P(A or B = P(A + P(B if the events cannot occur at the same time (mutually exclusive P(A and B = P(A P(B P( A = 1 P(A P(A or B = P(A + P(B P(A and B if the events can occur at the same time Learners must identify sources of bias, errors in measurement, and potential uses and misuses of statistics and charts and their effects. Learners must also communicate conclusions and predictions that can be made from the analysis of data 1. The events A and B are mutually exclusive such that P(B.P(A and P(A B 0,65 Find P(B. 2. David has a box with 25 items and says that if Ryan puts his hand inside the box and selects one item, then: P(pen 1, P(pencil 0,P(blue pen 0, 8 and P(red pen 0, 2 What does David have in the box?
2 . The pie-chart shows the number of overseas visitors to Cape Town in December Determine: (a The total number of visitors to Cape Town in December U.K. U.S.A Other Japan (b The probability that if one visitor was chosen at random, he would be from Japan.. A survey was conducted with forty-six pupils in a class. Twenty-four pupils like watching rugby, and thirty pupils like watching soccer. Thirty-six pupils like watching rugby or soccer, or both. (a Draw a Venn Diagram to illustrate the given data. (b Hence, or otherwise, calculate the probability that a pupil in the class, chosen at random (1 likes watching neither rugby nor soccer? (2 likes watching rugby, but not soccer? ( likes watching both rugby and soccer?
3 5. Estimate the probability for each event listed below. State if the probability is impossible, below average, a chance, above average, certain, or if it is impossible to tell from the information given. Event A: Event B: Event C: Event D: Event E: A mouse will be the next cricket captain The next baby born will be a girl SA will win the next rugby World Cup A pentagon will have five sides If you roll a die, the score will be a prime number 6. Below is a news article about the production of maize in South Africa in 200 and 200. (a What is the percentage decrease in maize production between 200 and 200? (b How many hectares of yellow maize were planted in 200? (c What is the per hectare production rate for wheat in 200?
4 7. Mr Smith has a camera to give to one of his pupils after a recent competition. The names of his pupils, and their ages are listed below. BOYS AGE GIRLS AGE David 1 Susan 16 Donovan 15 Denise 1 George 16 Beverley 15 Denis 15 Kristin 15 Andrew 16 Allison 15 Derrick 15 Kerri-Lee 15 Ryan 15 (a Write down n(s. (b Events are defined as follows: E 1: E 2: E : E : A girl will win A 15-year old will win The winner s name starts with D A 16-year old boy will win Determine (1 P( E 1 (2 P( E ( P( E ( P( E1or E (5 P( E1or E (6 P(E 2 and E
5 8. In a recent municipal election, a graph was printed on a pamphlet by one of the parties. The graph shows the results of a voter poll of an opposition candidate, Ray Smith. Percentage of voters choosing Ray March April May June Mar April May June (a According to the table, is Ray Smith losing or gaining in popularity? Motivate your answer. (b What impression is given by the graph? Motivate your answer. (c Do you think the impression created by the graph is intentional? Motivate your answer. (d Draw a graph which gives a fair impression.
6 SOLUTIONS 1. P(A or B P(A + P(B 0,65 P(A.P(A 5.P(A P(A 0,1 P(B 0,52 2. P(blue or red pen 0,8 + 0,2 1 David has 20 blue pens and 5 red pens in the box.. (a people 1 5people people 680 people people 10 Thus Other people U.K. U.S.A Other Japan Thus Total is 190 people. (b P(Japan
7 (a S (b ( ( ( rugby 18 soccer 5 A: impossible B: chance C: above average D: certain E: chance 6 (a (9,71 8,98 0, 77 0,77 % decrease 100 7,68 % 9,71,21 (b hectares 8,98 (c 8, tons per hectare
8 7 (a 1 6 (b (1 P( E 1 = 1 (2 P( E ( P( E 1 ( P( E 1 or E = P( E 1 + P( E P( E1and E = = 1 (5 P( E 1 + P(E P( E1and E = = 169 (6 P(E 2 and E = P(E 2 P(E 8 5 = = 169 Mar
9 8. (a Gaining. From March to June the percentage of voters increased from 20% to 5%. (b Ray s popularity is decreasing. The slope of the graph gives an incorrect impression. (c Probably (yes to give an impression that their own candidate is gaining popularity. (d June May April March
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