Maths Level 4 Module 13

Mathematics NQF Level 4 *see terms and conditions Downloaded from hlayiso.com Mathematics NQF Level 4

Data handling and probability models Topic 4 Downloaded from hlayiso.com Mathematics NQF Level 4

Use experiments, simulations and probability distribution to set and explore probability models Module 13 Downloaded from hlayiso.com Mathematics NQF Level 4

Learning activity 13.2 Downloaded from hlayiso.com Mathematics NQF Level 4

Venn diagram – vid 24 Downloaded from hlayiso.com Learning activity 13.2

Learning activity 13.3 Downloaded from hlayiso.com Mathematics NQF Level 4

Tree diagram – vid 23 Downloaded from hlayiso.com Learning activity 13.3

Summative assessment Module 13 Downloaded from hlayiso.com Mathematics NQF Level 4

1) There are 450 boys in a school. 250 play soccer and 90 play cricket. 50 play cricket and soccer. 1.1) Draw a Venn diagram of the information. Figure 13.8 Downloaded from hlayiso.com Summative assessment – Module 13

1.2 Determine: a) P(soccer) 250 p(s) = 450 = 0,556 b) P(soccer and cricket) 50 p(s and c) = 450 = 0,111 Downloaded from hlayiso.com Summative assessment – Module 13

1.2 (Continued) c) P(soccer or cricket) 290 p(s or c) = 450 = 0, 644 d) P(not playing soccer) 1 200 p(s ) = 450 = 0, 444 Downloaded from hlayiso.com Summative assessment – Module 13

2) A box contains 12 identical balls, of which four are white and eight are red. The sample space is S S = {W1 ; W2 ; W3 ; W4 ; R1 ; R 2 ; R 3 ; R 4 ; R 5 ; R 6 ; R 7 ; R 8 } Calculate the probability of drawing: 2a) A white ball n(W) p (W) = n(S) 4 = 12 = 0,333 Downloaded from hlayiso.com Summative assessment – Module 13

2b) A red ball n( R ) p( R) = n(S) 8 = 12 = 0, 667 Downloaded from hlayiso.com Summative assessment – Module 13

3) A box contains six balls: two white ones, three red ones and one blue one. Two balls are drawn from the box. From a tree diagram n(S) = 30; n(r and r) = 6; n(b and b) = 0; n(W) = 18; n(w and r) = 12 Downloaded from hlayiso.com Summative assessment – Module 13

3) Continued Determine the probability of the following: 3a) Both balls being red 6 p (r and r ) = 30 2 = 10 = 0, 2 3b) Both balls being blue 0 p (b and b) = 30 =0 Downloaded from hlayiso.com Summative assessment – Module 13

3) Continued 3c) One ball being white 18 p ( w) = 30 3 = 5 = 0, 6 3d) One white and one red ball being drawn 12 p ( w and r) = 30 2 = 5 0.4 =Downloaded from hlayiso.com Summative assessment – Module 13

4) A coin is tossed and a die is rolled. 4.1) Show this event on a tree diagram. Figure 13.9 Downloaded from hlayiso.com Summative assessment – Module 13

4.2) Determine the probability of obtaining “heads” and an even number. 3 p (H; even) = 12 = 0, 25 4.3) Determine the probability of obtaining “heads” and a 4. 1 p (H; 4) = 12 = 0, 0833 Downloaded from hlayiso.com Summative assessment – Module 13

4.4) Determine the probability of obtaining “tails” and an uneven number. 3 p (T ; uneven) = 12 = 0, 25 Downloaded from hlayiso.com Summative assessment – Module 13

5) The following two-way table contains results of a survey investigating the effect of smoking on lung cancer: Effect on lung cancer Male (M) Female (F) Total Positive result (P) 70 60 130 Negative result (N) 42 49 91 Total 112 109 221 Downloaded from hlayiso.com Summative assessment – Module 13

5a) Use the original table and calculate P(M) × P(P). 112 130 p (male) ⋅ p (pos) = × 221 221 14 560 = 48 841 = 0, 298 5b) Calculate P(M and P). 70 p (male and pos) = 221 = 0,317 Downloaded from hlayiso.com Summative assessment – Module 13

5c) Change the expected numbers in the cells for the data to be more independent. The totals must stay the same. Ratio 112:109 112 ∴ The positive male result must be ×130 221 14 560 = 221 Male Female Total = 65,88 (66) Positive result 66 64 130 No positive result 46 45 91 Total 112 109 221 Downloaded from hlayiso.com Summative assessment – Module 13

Mathematics NQF Level 2 Downloaded from hlayiso.com Mathematics NQF Level 4