In Dice Game, you must run across a 140m bridge before it collapses. You are given two 6- sided dices with these numbers on their faces:

-8, -7, 1, 2, 7, 8 on the first dice

-7, -2, 1, 3, 7, 7 on the second dice

At every move, you throw the two dice simultaneously to obtain a score of X which is the product of the top faces of the two dice. You are then required to run forward X meters across the bridge. If unfortunately, X is negative, you need to run backward X meters.

You can only make 3 moves before the bridge collapses.

For example, if you throw (8, 7), (2, -2) and (-7, -7), you will have run a total of 101m (since 8 x 7 + 2 x (-2) + (-7) x (-7) = 56 â€“ 4 + 49 = 101). Sadly, this means you will still be on the bridge when it collapses.

**You are not allowed to import any packages in this question unless stated otherwise.**

(a) List the unique scores X you can get per move in ascending order.

(b) Code a function pmf(x) that returns P(X = x). Compute to 6 decimal places the values

P(X = -21)

P(X = -14)

P(X = 14)

P(X = 50)

(c) Code a function cdf(x) that returns P(X x). Compute to 6 significant figuresthe values

P(X -21)

P(X < -14)

P(X

P(X < 50)

(d) What is the probability of you crossing the bridge successfully? Explain your reasoning clearly. Give your answer correct to 6 significant figures.

(e) Draw and label the step graphs of pmf(x) and cdf(x) for an integer x such that â€“ x matplotlib.pyplot.