Q1) A 'typing monkey' is one who randomly pushes keys on the keyboard hoping to make one sensible sentence. Within the English language there are 26 alphabets and 14 punctuation marks. Assuming that (i) subsequent characters (alphabets and punctuations) are independent of one another, and (ii) all characters are equally likely, what is the likelihood that the following sentences will be typed by the typing monkey?

A. Pakistan is a great country.

B. The Universe was created out of pure chance.

Q2) Suppose our typist monkey is typing randomly 24/7 at the rate of one character per second. The typing monkey is on a mission to write the constitution of Pakistan which contains 10,000,000 characters.

A. What is the probability that the typist monkey will write the same constitution verbatim?

B. Let us assume that the typist monkey did in fact manage to write the document. How many days will it take him to do the same?

Q3) Suppose atoms of the universe are hitting one another purely randomly. Furthermore, let us assume that likelihood of atoms hitting one another with enough energy to cause chemical reactions is quantified by value . Hence, the likelihood of two atoms hitting one another without causing a chemical reaction is 1 = . As of now (2021), it is estimated that the observable universe has about 10⁸⁰ atoms.

A. Assuming two reactions are independent of one another, what is the probability that the atoms hitting together randomly will in fact produce the same universe as is present today?

B. Let us assume that the universe does exist (which it does, because you seem to be present OR is this MATRIX 4) and 1 chemical reaction takes place in 1 second. How many years will it take the universe to form?

Thinking Problem: Given your answers to Q1, Q2 and Q3, what is your opinion on the statement "The Universe was created out of pure chance" - given in Q1 (B)?