Question $1$

$($Recall that a regular deck of $52$ cards consists of $13$ kinds$/$denominations$,$ each having $4$ suits: $,,.)$

Suppose you take $3$ cards from a regular deck of cards, one card at a time, without replacement $($i$.$e$.$ without putting any card back$).$

Part a$)$

What is the probability that the first, the second and the third card drawn are a Queen, a King and an Ace, respectively $($i$.$e$.$ in that order$)?$ Do NOT round your answer.

Write your answer as

ans $=$

For example, if you think the answer is $1/36$ you should create variable ans as

ans $=1/36$

IMPORTANT: Just typing $1/36,$ or answer $=1/36$ is not acceptable. Also, do NOT put dot at the end $($this is a python code, not a sentence in English$).$ Your answer will be graded automatically, and the test code expects you to create a Python variable called ans, and the code will test the value of ans.

$$

# your code here

raise NotImplementedError

$$

$"""$Check whether the answer is numeric and from the interval $[0,1]-$ since it's a probability"""

$$

assert isinstance$($ans$,$float$)$

assert $(0<=$ ans$)$ & $($ans $<=1),$ "Sorry, the answer should be a probability, which means a number from $[0,1]"$

$$

$"""$Check whether the answer is correct $($hidden test$)"""$

$$

$$

Part b$)$

What is the probability that the first, the second and the third card drawn are Queen, Queen and Ace, in that order? Do NOT round your answer.

Write your answer as

ans $=$

# your code here

raise NotImplementedError

$$

$"""$Check whether the answer is numeric and from the interval $[0,1]-$ since it's a probability"""

$$

assert isinstance$($ans$,$float$)$

assert $(0<=$ ans$)$ & $($ans $<=1),$ "Sorry, the answer should be a probability, which means a number from $[0,1]"$

$$

$"""$Check whether the answer is correct $($hidden test$)"""$

$$

$$

Question $2$

Consider two boxes, one containing $3$ blue and $2$ red marbles, the other contains $3$ blue and $5$ red marbles. A box is selected at random, and a marble is drawn from it at random.

Part a$)$

What is the probability that the selected marble is blue? Do NOT round your answer.

Create a variable pB that stores the value of this probability. That is$,$ write your answer as

pB $=$

$$

# your code here

raise NotImplementedError

$$

$"""$Check whether the answer is numeric and from the interval $[0,1]-$ since it's a probability"""

$$

assert isinstance$($pB$,$float$)$

assert $(0<=$ pB$)$ & $($pB $<=1),$ "Sorry, the answer should be a probability, which means a number from $[0,1]"$

$$

$"""$Check whether the answer is correct $($hidden test$)"""$

$$

$$

Part b$)$

If the chosen marble is blue, what is the probability that it was taken from the first box? Do NOT round your answer.

Create a variable pFgivenB which is equal to the desired probability.

pFgivenB $=$