Add exam fall 2019

src/content/evaluations/comp2804/exam-fall-2019.md

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+---
+title: Exam Fall 2019
+path: comp2804/exam-fall-2019
+author: Michiel Smid
+course: comp2804
+questions:
+  - comp2804/exam-fall-2019/1
+  - comp2804/exam-fall-2019/2
+  - comp2804/exam-fall-2019/3
+  - comp2804/exam-fall-2019/4
+  - comp2804/exam-fall-2019/5
+  - comp2804/exam-fall-2019/6
+  - comp2804/exam-fall-2019/7
+  - comp2804/exam-fall-2019/8
+  - comp2804/exam-fall-2019/9
+  - comp2804/exam-fall-2019/10
+  - comp2804/exam-fall-2019/11
+  - comp2804/exam-fall-2019/12
+  - comp2804/exam-fall-2019/13
+  - comp2804/exam-fall-2019/14
+  - comp2804/exam-fall-2019/15
+  - comp2804/exam-fall-2019/16
+  - comp2804/exam-fall-2019/17
+  - comp2804/exam-fall-2019/18
+  - comp2804/exam-fall-2019/19
+  - comp2804/exam-fall-2019/20
+  - comp2804/exam-fall-2019/21
+  - comp2804/exam-fall-2019/22
+  - comp2804/exam-fall-2019/23
+  - comp2804/exam-fall-2019/24
+  - comp2804/exam-fall-2019/25
+---

src/content/questions/comp2804/exam-fall-2019/1/index.md

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+---
+title: N/A
+path: comp2804/exam-fall-2019/1
+type: multiple-choice
+author: Michiel Smid
+question: comp2804/exam-fall-2019/1/question.ts
+tags:
+  - comp2804
+---

src/content/questions/comp2804/exam-fall-2019/1/question.ts

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+import type { MultipleChoiceQuestion } from "@common/MultipleChoiceQuestionGenerator";
+
+const body = String.raw`
+Consider strings of length 85, in which each character is one of the letters $a,b,c,d$. <br>
+		How many such strings have exactly 5 letters $c$?
+`;
+
+const label1 = "${85 \\choose 5} \\cdot 3^{80}$";
+const label2 = "${85 \\choose 5} \\cdot 3^{85}$";
+const label3 = "${85 \\choose 5} \\cdot 4^{80}$";
+const label4 = "${85 \\choose 5} \\cdot 4^{85}$";
+
+export const question: MultipleChoiceQuestion = {
+  body: body,
+  options: [
+    { label: label1, correct: true },
+    { label: label2, correct: false },
+    { label: label3, correct: false },
+    { label: label4, correct: false },
+  ],
+};

src/content/questions/comp2804/exam-fall-2019/10/index.md

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+---
+title: N/A
+path: comp2804/exam-fall-2019/10
+type: multiple-choice
+author: Michiel Smid
+question: comp2804/exam-fall-2019/10/question.ts
+tags:
+  - comp2804
+---

src/content/questions/comp2804/exam-fall-2019/10/question.ts

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+import type { MultipleChoiceQuestion } from "@common/MultipleChoiceQuestionGenerator";
+
+const body = String.raw`
+<div hidden>
+			$\newcommand{\IFeelLikeSinging}{{\rm IF {\scriptsize EEL} L {\scriptsize IKE} S {\scriptsize INGING}}}$
+		</div>
+		
+		Consider the recursive algorithm $\IFeelLikeSinging$, which takes as input an integer $n \geq 0$:
+		
+		<p>
+			$\IFeelLikeSinging(n):$ <br>
+			$\quad \mathbf{if}\ n = 0\ \mathrm{or}\ n = 1\ \mathbf{then}$ <br>
+			$\quad \quad \text{sing O Canada}$ <br>
+			$\quad \mathbf{else}\ \mathbf{if}\ n\ \text{is odd}\ \mathbf{then}$ <br>
+			$\quad \quad \IFeelLikeSinging(n + 1)$ <br>
+			$\quad \mathbf{else}$ <br>
+			$\quad \quad \IFeelLikeSinging(\frac{n}{2})$ <br>
+			$\quad \quad \IFeelLikeSinging(\frac{n}{2} - 1)$ <br>
+		</p>
+		
+		If you run algorithm $\IFeelLikeSinging(9)$, how many times do you sing O Canada?
+`;
+
+const label1 = String.raw`6`;
+const label2 = String.raw`7`;
+const label3 = String.raw`8`;
+const label4 = String.raw`9`;
+
+export const question: MultipleChoiceQuestion = {
+  body: body,
+  options: [
+    { label: label1, correct: false },
+    { label: label2, correct: false },
+    { label: label3, correct: true },
+    { label: label4, correct: false },
+  ],
+};

src/content/questions/comp2804/exam-fall-2019/11/index.md

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+---
+title: N/A
+path: comp2804/exam-fall-2019/11
+type: multiple-choice
+author: Michiel Smid
+question: comp2804/exam-fall-2019/11/question.ts
+tags:
+  - comp2804
+---

src/content/questions/comp2804/exam-fall-2019/11/question.ts

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+import type { MultipleChoiceQuestion } from "@common/MultipleChoiceQuestionGenerator";
+
+const body = String.raw`
+Assume you write a multiple-choice exam that has 25 questions. For each question, four options are given
+		to you, and exactly one of these options is the correct answer. Assume that you answer each question
+		uniformly at random, where the choices for different questions are independent of each other. What is the
+		probability that you have exactly 17 correct answers?
+`;
+
+const label1 = "${25 \\choose 17} \\cdot \\left( 1 \\middle/ 4 \\right)^{17}$";
+const label2 = "${25 \\choose 17} \\cdot \\left( 3 \\middle/ 4 \\right)^{17}$";
+const label3 =
+  "${25 \\choose 17} \\cdot \\left( 1 \\middle/ 4 \\right)^{17} \\cdot \\left( 3 \\middle/ 4 \\right)^8$";
+const label4 =
+  "${25 \\choose 17} \\cdot \\left( 1 \\middle/ 4 \\right)^8 \\cdot \\left( 3 \\middle/ 4 \\right)^{17}$";
+
+export const question: MultipleChoiceQuestion = {
+  body: body,
+  options: [
+    { label: label1, correct: false },
+    { label: label2, correct: false },
+    { label: label3, correct: true },
+    { label: label4, correct: false },
+  ],
+};

src/content/questions/comp2804/exam-fall-2019/12/index.md

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+---
+title: N/A
+path: comp2804/exam-fall-2019/12
+type: multiple-choice
+author: Michiel Smid
+question: comp2804/exam-fall-2019/12/question.ts
+tags:
+  - comp2804
+---

src/content/questions/comp2804/exam-fall-2019/12/question.ts

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+import type { MultipleChoiceQuestion } from "@common/MultipleChoiceQuestionGenerator";
+
+const body = String.raw`
+Consider a uniformly random bitstring of length 5. Define the events
+		
+		[defs]
+			A = "the first three bits are 101 or 110",
+			B = "the last three bits are 111".
+		[/defs]
+		
+		Which of the following is true?
+`;
+
+const label1 = String.raw`The events $A$ and $B$ are independent.`;
+const label2 = String.raw`The events $A$ and $B$ are not independent.`;
+const label3 = String.raw`None of the above.`;
+
+export const question: MultipleChoiceQuestion = {
+  body: body,
+  options: [
+    { label: label1, correct: true },
+    { label: label2, correct: false },
+    { label: label3, correct: false },
+  ],
+};

src/content/questions/comp2804/exam-fall-2019/13/index.md

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+---
+title: N/A
+path: comp2804/exam-fall-2019/13
+type: multiple-choice
+author: Michiel Smid
+question: comp2804/exam-fall-2019/13/question.ts
+tags:
+  - comp2804
+---

src/content/questions/comp2804/exam-fall-2019/13/question.ts

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+import type { MultipleChoiceQuestion } from "@common/MultipleChoiceQuestionGenerator";
+
+const body = String.raw`
+A certain terrible, no-good, mean-spirited, awful professor gives his students 250 sample exam questions
+		and then makes his final exam by choosing 25 of these questions uniformly at random. Student Nika doesn't
+		have much time to study so she chooses 50 (out of 250) random sample exam questions and practices on those.
+		
+		<p style="margin: 0.5rem 0;">
+			When Nika writes the exam, what is the expected number of questions that appear on the exam and that
+			Nika has practiced on?
+		</p>
+		
+		(n.b., depending on your background, it may be helpful to observe that this can be modelled using the hypergeometric
+		distribution)
+`;
+
+const label1 = String.raw`2`;
+const label2 = String.raw`5`;
+const label3 = String.raw`10`;
+const label4 = String.raw`20`;
+
+export const question: MultipleChoiceQuestion = {
+  body: body,
+  options: [
+    { label: label1, correct: false },
+    { label: label2, correct: true },
+    { label: label3, correct: false },
+    { label: label4, correct: false },
+  ],
+};

src/content/questions/comp2804/exam-fall-2019/14/index.md

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+---
+title: N/A
+path: comp2804/exam-fall-2019/14
+type: multiple-choice
+author: Michiel Smid
+question: comp2804/exam-fall-2019/14/question.ts
+tags:
+  - comp2804
+---

src/content/questions/comp2804/exam-fall-2019/14/question.ts

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+import type { MultipleChoiceQuestion } from "@common/MultipleChoiceQuestionGenerator";
+
+const body = String.raw`
+Continuing from the previous question, what is the probability that Nika has not practiced on any of the
+		actual exam questions?
+`;
+
+const label1 = String.raw`0`;
+const label2 = String.raw`$\left. {225 \choose 50} \middle/ {250 \choose 50} \right.$`;
+const label3 = String.raw`$\left. {225 \choose 25} \middle/ {250 \choose 50} \right.$`;
+const label4 = String.raw`$\left. {225 \choose 25} \middle/ {225 \choose 50} \right.$`;
+
+export const question: MultipleChoiceQuestion = {
+  body: body,
+  options: [
+    { label: label1, correct: false },
+    { label: label2, correct: true },
+    { label: label3, correct: false },
+    { label: label4, correct: false },
+  ],
+};

src/content/questions/comp2804/exam-fall-2019/15/index.md

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+---
+title: N/A
+path: comp2804/exam-fall-2019/15
+type: multiple-choice
+author: Michiel Smid
+question: comp2804/exam-fall-2019/15/question.ts
+tags:
+  - comp2804
+---

src/content/questions/comp2804/exam-fall-2019/15/question.ts

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+import type { MultipleChoiceQuestion } from "@common/MultipleChoiceQuestionGenerator";
+
+const body = String.raw`
+A bowl contains 5 blue balls and 4 red balls. We choose 2 balls uniformly at random. Define the events
+		
+		[defs]
+		  A = "both balls are red",
+		  B = "both balls have the same color".
+		[/defs]
+		
+		What is the conditional probability $\Pr(A|B)$?
+`;
+
+const label1 = String.raw`$\frac{{4 \choose 2}}{{5 \choose 2} + {4 \choose 2}}$`;
+const label2 = String.raw`$\frac{{5 \choose 2} + {4 \choose 2}}{{4 \choose 2}}$`;
+const label3 = String.raw`$\frac{{4 \choose 2}}{{9 \choose 2}}$`;
+const label4 = String.raw`$\frac{{4 \choose 2}}{{5 \choose 2} \cdot {4 \choose 2}}$`;
+
+export const question: MultipleChoiceQuestion = {
+  body: body,
+  options: [
+    { label: label1, correct: true },
+    { label: label2, correct: false },
+    { label: label3, correct: false },
+    { label: label4, correct: false },
+  ],
+};

src/content/questions/comp2804/exam-fall-2019/16/index.md

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+---
+title: N/A
+path: comp2804/exam-fall-2019/16
+type: multiple-choice
+author: Michiel Smid
+question: comp2804/exam-fall-2019/16/question.ts
+tags:
+  - comp2804
+---

src/content/questions/comp2804/exam-fall-2019/16/question.ts

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+import type { MultipleChoiceQuestion } from "@common/MultipleChoiceQuestionGenerator";
+
+const body = String.raw`
+We choose an element $x$ uniformly at random from the set $\{1,2,3,...,10\}$. Define the events
+		
+		[defs]
+		  A = "$x$ is even",
+		  B = "$x$ is divisible by 3".
+		[/defs]
+		
+		What is the conditional probability $\Pr(A|B)$?
+`;
+
+const label1 = String.raw`3/10`;
+const label2 = String.raw`1/3`;
+const label3 = String.raw`1/2`;
+const label4 = String.raw`2/3`;
+
+export const question: MultipleChoiceQuestion = {
+  body: body,
+  options: [
+    { label: label1, correct: false },
+    { label: label2, correct: true },
+    { label: label3, correct: false },
+    { label: label4, correct: false },
+  ],
+};

src/content/questions/comp2804/exam-fall-2019/17/index.md

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+---
+title: N/A
+path: comp2804/exam-fall-2019/17
+type: multiple-choice
+author: Michiel Smid
+question: comp2804/exam-fall-2019/17/question.ts
+tags:
+  - comp2804
+---

src/content/questions/comp2804/exam-fall-2019/17/question.ts

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+import type { MultipleChoiceQuestion } from "@common/MultipleChoiceQuestionGenerator";
+
+const body = String.raw`
+We choose an element $x$ uniformly at random from the set $\{1,2,3,...,10\}$. Define the events
+		
+		[defs]
+		  A = "$x$ is even",
+		  B = "$1 \leq x \leq 5$".
+		[/defs]
+		
+		Which of the following is true?
+`;
+
+const label1 = String.raw`The events $A$ and $B$ are independent.`;
+const label2 = String.raw`The events $A$ and $B$ are not independent.`;
+const label3 = String.raw`None of the above.`;
+
+export const question: MultipleChoiceQuestion = {
+  body: body,
+  options: [
+    { label: label1, correct: false },
+    { label: label2, correct: true },
+    { label: label3, correct: false },
+  ],
+};

src/content/questions/comp2804/exam-fall-2019/18/index.md

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+---
+title: N/A
+path: comp2804/exam-fall-2019/18
+type: multiple-choice
+author: Michiel Smid
+question: comp2804/exam-fall-2019/18/question.ts
+tags:
+  - comp2804
+---