Q$3$: Throw Dice $-30$ pts

Consider that you are throwing a pair of dice. A single die yields values between $1$ and $6$

$($inclusive$),$ so a pair of dice yields a total between $2$ and $12.$ However, the probabilities of the

total being $2,3,...,12$ are not equal. You will have a total of $12$ with probability $1/36($only

possibility is $6+6=12),$ but you will have a total of $7$ with probability $6/36$ since there are multiple

outcomes that cause a total of $7($dice outcomes: $1-6,2-5,3-4,4-3,5-2,6-1).$

Open ThrowDice.py that is given to you. Here, you will see that we gave you the function to

throw a $*$single$*$ die: throw$\_$single$\_$die. Do not modify this function. Use this function when

throwing a pair of dice. Solve the following parts.

Part A $(10$ pts$)$: Implement the function record$\_$dice$\_$throws$($throws$).$

$$ The input parameter throws denotes how many times the pair of dice is thrown.

$$ Your function should return a dictionary in which the keys of the dictionary are tuples

$($first$\_$die, second$\_$die$)$ and the values are the number of times the corresponding dice

outcome is observed.

For example, when throws$=10000,$ the return value may look like this:

This means the outcome $(1,1)$ was observed $260$ times, the outcome $(1,2)$ was observed

$255$ times, $...,$ and the outcome $(6,6)$ was observed $256$ times.

Part B $(10$ pts$)$: Implement the function calculate$\_$frequencies$($throws$\_$dict$)$ such that:

$$ The input parameter throws$\_$dict is the dictionary created in Part A$.$

$$ The function returns a list of tuples, each tuple consists of two elements:

$$ The first element is the total of two dice

$$ The second element is the ratio of cases in which that total was observed

Continuing from the above example, the return value of this function looks like this:

This means the total$=2$ was observed in $2\mathrm{.}6\%$ of the dice throws, total$=3$ was observed in

$5\mathrm{.}35\%$ of the dice throws, $...,$ total$=7$ was observed in $16\mathrm{.}82\%$ of the dice throws, $...,$ and

total$=12$ was observed in $2\mathrm{.}56\%$ of the dice throws.

Since the minimum total is $2($because $1+1=2)$ and the maximum total is $12($because $6+6=12),$

there are guaranteed to be $11$ tuples in the returned list.

Hint: Sum of the normalized frequencies in this list should add up to $1.$ You can use this fact

to check the correctness of your results.

Part C $(10$ pts$)$: Implement the function write$\_$dict$\_$to$\_$file$($throws$\_$dict$)$ to write the above

created dictionary to a file.

$$ The input parameter throws$\_$dict is the dictionary created in Part A$.$

$$ Your function should create and write the above dictionary to a file called

$$diceresults$.$txt$$ in the following format:

The contents of diceresults.txt is a $6$x$6$ matrix corresponding to the counts of:

$(1,1),(1,2),...,(1,6)$ in the first row separated by commas

$(2,1),(2,2),...,(2,6)$ in the second row separated by commas

$...$

$(6,1),(6,2),...,(6,6)$ in the sixth row separated by commas