Update questions to the new .xml format app/src/data/questions (#207)

* Converted to new format

* Delete .idea directory

app/src/data/questions/comp2804/exam-fall-2014/exam-fall-2014.json

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+{ 
+    "id": "exam-fall-2014",
+    "title": "Fall 2014 Exam",
+    "Author": "Michiel Smid",
+    "questions": [
+		"comp2804/exam-fall-2014/f14f01.xml",
+		"comp2804/exam-fall-2014/f14f02.xml",
+		"comp2804/exam-fall-2014/f14f03.xml",
+		"comp2804/exam-fall-2014/f14f04.xml",
+		"comp2804/exam-fall-2014/f14f05.xml",
+		"comp2804/exam-fall-2014/f14f06.xml",
+		"comp2804/exam-fall-2014/f14f07.xml",
+		"comp2804/exam-fall-2014/f14f08.xml",
+		"comp2804/exam-fall-2014/f14f09.xml",
+		"comp2804/exam-fall-2014/f14f10.xml",
+		"comp2804/exam-fall-2014/f14f11.xml",
+		"comp2804/exam-fall-2014/f14f12.xml",
+		"comp2804/exam-fall-2014/f14f13.xml",
+		"comp2804/exam-fall-2014/f14f14.xml",
+		"comp2804/exam-fall-2014/f14f15.xml",
+		"comp2804/exam-fall-2014/f14f16.xml",
+		"comp2804/exam-fall-2014/f14f17.xml",
+		"comp2804/exam-fall-2014/f14f18.xml",
+		"comp2804/exam-fall-2014/f14f19.xml",
+		"comp2804/exam-fall-2014/f14f20.xml",
+		"comp2804/exam-fall-2014/f14f21.xml",
+		"comp2804/exam-fall-2014/f14f22.xml",
+		"comp2804/exam-fall-2014/f14f23.xml",
+		"comp2804/exam-fall-2014/f14f24.xml",
+		"comp2804/exam-fall-2014/f14f25.xml"
+	]
+}

app/src/data/questions/comp2804/exam-fall-2014/f14f01.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		A password consists of 13 characters, each character being one of the ten digits $0,1,2,\dots,9$. <br>
+		A password must contain exactly one odd digit. How many passwords are there?
+	]]>
+	</question>
+	<answer correct="false">$13 \cdot 5^{12}$</answer>
+	<answer correct="true">$13 \cdot 5^{13}$</answer>
+	<answer correct="false">$13 \cdot 9^{12}$</answer>
+	<answer correct="false">$13 \cdot 5 \cdot 9^{12}$</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f02.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		A password consists of 13 characters, each character being one of the ten digits $0,1,2,\dots,9$. <br>
+		A password must contain at least one odd digit and at most two even digits. How many passwords are
+		there?
+	]]>
+	</question>
+	<answer correct="false">$5^{12} + 13 \cdot 5^{12} + {13 \choose 2}5^{12}$</answer>
+	<answer correct="false">$5^{13} + 13 \cdot 9^{12} + {13 \choose 2}9^{12}$</answer>
+	<answer correct="true">$5^{13} + 13 \cdot 5^{13} + {13 \choose 2}5^{13}$</answer>
+	<answer correct="false">$5 \cdot 9^{12} + 13 \cdot 5 \cdot 9^{12} + {13 \choose 2}5 \cdot 9^{12}$</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f03.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		What is
+		$$
+			\sum_{k = 0}^{45} {45 \choose k}(-3)^{2k}.
+		$$
+	]]>
+	</question>
+	<answer correct="false">$(-2)^{45}$</answer>
+	<answer correct="false">$4^{45}$</answer>
+	<answer correct="false">$(-8)^{45}$</answer>
+	<answer correct="true">$10^{45}$</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f04.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		How many bitstings of length 13 start with 010 or end with 11?
+	]]>
+	</question>
+	<answer correct="false">$2^{10} + 2^{11}$</answer>
+	<answer correct="true">$3 \cdot 2^{10} - 2^{8}$</answer>
+	<answer correct="false">$2^{13} - (2^{10} + 2^{11})$</answer>
+	<answer correct="false">None of the above.</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f05.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		Let $S_n$ be the number of bitstrings of length $n$ that do not contain the substring 11. Which of
+		the following is true?
+	]]>
+	</question>
+	<answer correct="true">$S_n = S_{n-1} + S_{n-2}\ \mathrm{for}\ n \geq 3.$</answer>
+	<answer correct="false">$S_n = S_{n-1} + S_{n-3}\ \mathrm{for}\ n \geq 3.$</answer>
+	<answer correct="false">$S_n = S_{n-1} + S_{n-2} + S_{n-3}\ \mathrm{for}\ n \geq 3.$</answer>
+	<answer correct="false">$S_n = 2 \cdot S_{n-1}\ \mathrm{for}\ n \geq 3.$</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f06.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		In a group of 100 students,
+		<ul style="margin: 0.5rem 0;">
+			<li>
+				40 like 8:30am classes,
+			</li>
+			<li>
+				30 like the course COMP 2804,
+			</li>
+			<li>
+				50 do not like 8:30am classes and do not like the course COMP 2804.
+			</li>
+		</ul>
+		How many students in this group like 8:30am classes and like the course COMP 2804?
+	]]>
+	</question>
+	<answer correct="false">10</answer>
+	<answer correct="true">20</answer>
+	<answer correct="false">30</answer>
+	<answer correct="false">40</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f07.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		Consider $m \geq 7$ blue balls $B_1,B_2,\dots,B_m$ and $n \geq 7$ red balls $R_1,R_2,\dots,R_n$.
+		We pick 7 balls of the same color and arrange them on a horizontal line. (The order on the line
+		matters.) How many arrangements are there?
+	]]>
+	</question>
+	<answer correct="true">$7!{m \choose 7} + 7!{n \choose 7}$</answer>
+	<answer correct="false">$m!{m \choose 7} + n!{n \choose 7}$</answer>
+	<answer correct="false">$7!{m + n \choose 7}$</answer>
+	<answer correct="false">None of the above.</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f08.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		The number of different strings that can be made by reordering the 10 letters of the word AAABBCCCCC is
+	]]>
+	</question>
+	<answer correct="false">$10!$</answer>
+	<answer correct="true">$\frac{10!}{2!3!5!}$</answer>
+	<answer correct="false">${10 \choose 3}{10 \choose 2}{10 \choose 5}$</answer>
+	<answer correct="false">None of the above.</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f09.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		How many solutions are there to the equation $x_1 + x_2 + x_3 = 13$, where $x_1 \geq 0$, $x_2 \geq 0$,
+		$x_3 \geq 0$ are integers?
+	]]>
+	</question>
+	<answer correct="false">${13 \choose 2}$</answer>
+	<answer correct="false">${14 \choose 2}$</answer>
+	<answer correct="true">${15 \choose 2}$</answer>
+	<answer correct="false">${16 \choose 2}$</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f10.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		Consider the following recursive function:
+		<table style="margin: 1rem auto;">
+			<tbody>
+				<tr>
+					<td style="vertical-align: top;">$f(0) = $</td>
+					<td>$-17,$</td>
+				</tr>
+				<tr>
+					<td style="vertical-align: top;">$f(n) = $</td>
+					<td>$f(n - 1) + 8n - 2\; \ \text{for all}$ $\text{integers}\ n \geq 1.$</td>
+				</tr>
+			</tbody>
+		</table>
+		Which of the following is true?
+	]]>
+	</question>
+	<answer correct="false">for all $n \geq 0$: $f(n) = 3n^{2} - n - 17$</answer>
+	<answer correct="false">for all $n \geq 0$: $f(n) = 3n^{2} + n - 17$</answer>
+	<answer correct="false">for all $n \geq 0$: $f(n) = 4n^{2} - 2n - 17$</answer>
+	<answer correct="true">for all $n \geq 0$: $f(n) = 4n^{2} + 2n - 17$</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f11.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		<div hidden>
+			$\newcommand{\Fib}{{\rm F \scriptsize IB}}$
+		</div>
+		
+		Consider the recursive algorithm $\Fib$, which takes as input an
+		integer $n \geq 0$:
+		
+		<p>
+			$\mathbf{Algorithm}\ \Fib(n)\mathrm{:}$ <br>
+			$\mathbf{if}\ n = 0\ \mathrm{or}\ n = 1$ <br>
+			$\mathbf{then}\ f = n$ <br>
+			$\mathbf{else}\ f = \Fib(n - 1) + \Fib(n - 2)$ <br>
+			$\mathbf{endif};$ <br>
+			$\mathbf{return}\ f$ <br>
+		</p>
+		
+		If we run algorithm $\Fib(20)$, how many calls are there to $\Fib(16)$?
+	]]>
+	</question>
+	<answer correct="false">4</answer>
+	<answer correct="true">5</answer>
+	<answer correct="false">6</answer>
+	<answer correct="false">7</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f12.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		A bowl contains 5 blue balls, 4 red balls, and 6 green balls. We choose 2 balls uniformly at random.
+		What is the probability that these 2 balls have the same color?
+	]]>
+	</question>
+	<answer correct="true">$\frac{{5 \choose 2} + {4 \choose 2} + {6 \choose 2}}{{15 \choose 2}}$</answer>
+	<answer correct="false">$\frac{{15 \choose 2}}{{5 \choose 2} + {4 \choose 2} + {6 \choose 2}}$</answer>
+	<answer correct="false">$\frac{{5 \choose 2}{4 \choose 2}{6 \choose 2}}{{15 \choose 2}}$</answer>
+	<answer correct="false">$\frac{{15 \choose 2}}{{5 \choose 2}{4 \choose 2}{6 \choose 2}}$</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f13.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		Annie, Boris, and Charlie have random and independent birthdays. (We ignore leap years, so that a
+		year has 365 days.) What is the probability that Annie, Boris, and Charlie have the same birthday?
+	]]>
+	</question>
+	<answer correct="false">$\frac{1}{364 \cdot 365}$</answer>
+	<answer correct="true">$\frac{1}{365^2}$</answer>
+	<answer correct="false">$\frac{365}{364^{2}}$</answer>
+	<answer correct="false">$\frac{1}{365^{3}}$</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f14.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		We flip a fair coin repeatedly and independently, resulting in a sequence of heads ($H$) and tails
+		($T$). We stop flipping the coin as soon as this sequence contains one $H$ or eight $T$s. What is
+		the probability that this sequence contains at most 7 $T$s?
+	]]>
+	</question>
+	<answer correct="false">$1 - (1/2)^{7}$</answer>
+	<answer correct="false">$\sum_{k=0}^{7} (1/2)^{k}$</answer>
+	<answer correct="true">$\sum_{k=0}^{7} (1/2)^{k+1}$</answer>
+	<answer correct="false">None of the above.</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f15.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		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 $\Pr(A|B)$?
+	]]>
+	</question>
+	<answer correct="true">$\frac{{4 \choose 2}}{{5 \choose 2} + {4 \choose 2}}$</answer>
+	<answer correct="false">$\frac{{5 \choose 2} + {4 \choose 2}}{{4 \choose 2}}$</answer>
+	<answer correct="false">$\frac{{4 \choose 2}}{{9 \choose 2}}$</answer>
+	<answer correct="false">$\frac{{4 \choose 2}}{{5 \choose 2}{4 \choose 2}}$</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f16.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		We choose an element $x$ uniformly at random from the set $\{1,2,3,\dots,10\}$. Define the events
+		[defs]
+		  A = "$x$ is even",
+		  B = "$x$ is divisible by 3".
+		[/defs]
+		What is the conditional probability $\Pr(A|B)$?
+	]]>
+	</question>
+	<answer correct="false">3/10</answer>
+	<answer correct="true">1/3</answer>
+	<answer correct="false">1/2</answer>
+	<answer correct="false">2/3</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f17.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		We choose an element $x$ uniformly at random from the set $\{1,2,3,\dots,10\}$. Define the events
+		[defs]
+		  A = "$x$ is even"
+		[/defs]
+		and
+		[defs]
+		  B = "$1 \leq x \leq 5$".
+		[/defs]
+		Which of the following is true?
+	]]>
+	</question>
+	<answer correct="false">The events $A$ and $B$ are independent.</answer>
+	<answer correct="true">The events $A$ and $B$ are not independent.</answer>
+	<answer correct="false">None of the above.</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f18.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		We choose an element $x$ uniformly at random from the set $\{1,2,3,\dots,10\}$. Define the events
+		[defs]
+		  A = "$x$ is even"
+		[/defs]
+		and
+		[defs]
+		  B = "$1 \leq x \leq 6$".
+		[/defs]
+		Which of the following is true?
+	]]>
+	</question>
+	<answer correct="true">The events $A$ and $B$ are independent.</answer>
+	<answer correct="false">The events $A$ and $B$ are not independent.</answer>
+	<answer correct="false">None of the above.</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f19.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		When a couple has a child, this child is a boy with probability 1/2 and a girl with probability
+		1/2, independent of the gender of previous children. A couple stops having children as soon as
+		they have a child that has the same gender as their first child. Define the events
+		[defs]
+		  A = "the second child is a boy"
+		[/defs]
+		and
+		[defs]
+		  B = "the couple has at least three children and the third child is a boy".
+		[/defs]
+		Which of the following is true?
+	]]>
+	</question>
+	<answer correct="true">The events $A$ and $B$ are independent.</answer>
+	<answer correct="false">The events $A$ and $B$ are not independent.</answer>
+	<answer correct="false">None of the above.</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f20.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		Assume you answer the first question in this exam by choosing one of the four answers uniformly at random.
+		You answer the second question by choosing, again uniformly at random, one of the three answers you did not choose in
+		the first question. What is the probability that you answer the second question correctly?
+	]]>
+	</question>
+	<answer correct="false">$\frac{1}{3}$</answer>
+	<answer correct="true">$\frac{1}{4}$</answer>
+	<answer correct="false">$\frac{1}{4} \cdot \frac{1}{3} + \frac{3}{4} \cdot \frac{1}{4}$</answer>
+	<answer correct="false">None of the above.</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f21.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		I flip two fair and independent coins. If the first coin comes up tails, you lose \$1 (i.e., you win -\$1).
+		If the second coin comes up heads, you win \$2. (Thus, if the first coin comes up tails and the second coin
+		comes up heads, you win \$1.) Define the random variable $X$ to be the amount of dollars that you win. 
+		What is the expected value of $X$?
+	]]>
+	</question>
+	<answer correct="false">2</answer>
+	<answer correct="false">1</answer>
+	<answer correct="false">1/4</answer>
+	<answer correct="true">1/2</answer>
+</multiple-choice>

app/src/data/questions/comp2804/exam-fall-2014/f14f22.xml

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+<multiple-choice>
+	<question>
+	<![CDATA[
+		I flip a fair coin, independently, 6 times, resulting in a sequence of heads ($H$) and tails ($T$).
+		For each (consecutive) $HTH$ in this sequence, you win \$5.
+		Define the random variable $X$ to be the amount of dollars that you win. For example, if the
+		sequence is
+		$$
+			THTHTH,
+		$$
+		then $X = 10$. What is the expected value of $X$?
+	]]>
+	</question>
+	<answer correct="false">2/5</answer>
+	<answer correct="false">2</answer>
+	<answer correct="true">5/2</answer>
+	<answer correct="false">5</answer>
+</multiple-choice>