Question 2.
Take the same problem set-up as before, rolling a fair dice 10 times. What is the
chance that every roll is less than or equal to 5?

BEGIN QUESTION
name: q1_2
manual: false
[5]:
five_or_less
= 3
# SOLUTION
five_or_less
[5]:
3
Question 3.
Assume we are picking a lottery ticket. We must choose three distinct numbers from
1 to 100 and write them on a ticket. Next, someone picks three numbers one by one from a bowl
2

with numbers from 1 to 100 each time without putting the previous number back in. We win if our
numbers are all called in order.
If we decide to play the game and pick our numbers as 12, 14, and 89, what is the chance that we
win?
Our proposed answer:
(
3
100
)
3
Assign
lottery
to either 1, 2, or 3.
BEGIN QUESTION
name: q1_3
manual: false
[8]:
lottery
= 3
# SOLUTION
Question 4.
Assume we have two lists, list A and list B. List A contains the numbers [10,20,30],
while list B contains the numbers [10,20,30,40]. We choose one number from list A randomly and
one number from list B randomly.
What is the chance that the number we drew from list A is
larger than the number we drew from list B?

[11]:
list_chances
= 2
# SOLUTION
1.2
2. Monkeys Typing Shakespeare
(...or at least the string ”datascience”)
A monkey is banging repeatedly on the keys of a
typewriter. Each time, the monkey is equally likely to hit any of the 26 lowercase letters of the
English alphabet, regardless of what it has hit before. There are no other keys on the keyboard.
This question is inspired by a mathematical theorem called the Infinite monkey theorem (
https://
en.wikipedia.org/wiki/Infinite_monkey_theorem
), which postulates that if you put a monkey
in the situation described above for an infinite time, they will eventually type out all of Shakespeare’s
works.
Question 1.
Suppose the monkey hits the keyboard 11 times.
Compute the chance that the
monkey types the sequence
datascience
. (Call this
datascience_chance
.) Use algebra and type
in an arithmetic equation that Python can evalute.
BEGIN QUESTION
name: q2_1
manual: false
3

[1]:
datascience_chance
=
(
1/26
)
**11
#SOLUTION
datascience_chance
[1]:
2.7245398995795435e-16
Question 2.
Write a function called
simulate_key_strike
. It should take
no arguments
, and
it should return a random one-character string that is equally likely to be any of the 26 lower-case
English letters.
BEGIN QUESTION
name: q2_2
manual: false