Question $2$

Consider two boxes. Box A contains $7$ blue and $5$ red marbles, while box $B$ contains $6$ blue and

$8$ red marbles. A box is selected at random, and $4$ marbles are drawn from it at random.

Let $x=$ number of blue balls in the sample of $4$ marbles.

Part a$)$

Create a python function prob$()$ with only one input variable $k,$ and which for any

kin$\{0,1,2,3,4\}$ computes the value of $P(x=k).$ Do NOT round the output values

$P(x=k).$

PYTHON CODE MUST PASS ALL TEST BELOW

$""\text{'}"$Check whether function prob is defined and has input parameter k$"""$

assert callable$($prob$),$ "Sorry, you didn't define function prob$()"$

assert $(0$prob$(k=4))$&$(prob(k=4)1),$ "Sorry, prob$(4)$ is a probability, which means a number from $[0,1]"$

"Check whether all the probabilities sum up to $1"\text{'}"$

assert abs$($sum$($np$.$array$([$prob$($k$)$ for $k$ in range$(5)]))-1)<mn\; id="EditorElement\_282988">1</mn>$e$-8,$ "Sorry, sum of all prob$($k$),$ k$=0,1,2,3,4$ MUST b

NOTE: The quotation above finished off to say, "Sorry, sum of all prob$(k),k=0,1,2,3,4$ MUST be $1"$

"Check whether the $6$th decimal digit of prob$($k$=3)$ is $7"""$

assert $np*mod({\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(np.flr(prob(3)**10****6)),10)==7,$ "Sorry, wrong answer"