1. **State the problems:** - (ii) Write the sample space $S$. - (iii) Write the elements of $A$ and find $n(A)$. - (iv) Find the probability $p(A)$ of event $A$. - (v) Find the probability of obtaining a number not less than three. - Bearing and distance problems related to a scale diagram. - Complete the table for $y=3x-2$ and draw its graph. --- 2. **Sample space $S$:** The sample space $S$ is the set of all possible outcomes. Given: $$S = \{1, 2, 3, 4, 5, 6, 7\}$$ Number of elements in $S$ is $n(S) = 7$. --- 3. **Event $A$ and $n(A)$:** Given: $$A = \{1, 2, 3, 4, 5, 6, 7\}$$ Number of elements in $A$ is: $$n(A) = 7$$ --- 4. **Probability of event $A$:** Probability formula: $$p(A) = \frac{n(A)}{n(S)}$$ Since $A = S$, then: $$p(A) = \frac{7}{7} = 1$$ This means event $A$ is certain. --- 5. **Probability of obtaining a number not less than three:** Numbers not less than 3 are $\{3,4,5,6,7\}$. Number of favorable outcomes: $$n = 5$$ Probability: $$p = \frac{5}{7}$$ The user states $\frac{4}{7}$, but correct count is 5 numbers, so probability is $\frac{5}{7}$. --- 6. **Bearing and distance problems:** (i) Instrument to find bearing: **clinometer**. (ii) Bearing of office from gate is not numerically given, but can be found from the diagram (not provided here). (iii) Scale diagram with scale 1:10 means 1 cm represents 10 m. (iv) Using scale diagram, measure distance and bearing to Science Lab from gate. --- 7. **Triangle data:** - Gate to Office: 60 m, angle at Office 50°. - Gate to Science Lab: 80 m, angle at Gate 50°. Use Law of Cosines or Sines to find distance Office to Science Lab and bearing. --- 8. **Complete the table for $y=3x-2$:** Given: | x | -1 | 0 | 1 | 2 | 3 | |---|----|---|---|---|---| | y | ? | ? | ? | ? | ? | Calculate each: - $y(-1) = 3(-1) - 2 = -3 - 2 = -5$ - $y(0) = 3(0) - 2 = 0 - 2 = -2$ - $y(1) = 3(1) - 2 = 3 - 2 = 1$ - $y(2) = 3(2) - 2 = 6 - 2 = 4$ - $y(3) = 3(3) - 2 = 9 - 2 = 7$ Table completed: | x | -1 | 0 | 1 | 2 | 3 | |---|----|---|---|---|---| | y | -5 | -2| 1 | 4 | 7 | --- 9. **Graph of $y=3x-2$:** - Plot points from table. - Draw straight line through points. - This is a linear function with slope 3 and y-intercept -2. --- **Final answers:** - Sample space $S = \{1,2,3,4,5,6,7\}$, $n(S)=7$. - Event $A = \{1,2,3,4,5,6,7\}$, $n(A)=7$. - $p(A) = 1$. - Probability of number $\geq 3$ is $\frac{5}{7}$. - Instrument: clinometer. - Table for $y=3x-2$ completed as above.