CMI 2024 | Data Science | Part A | Question: 17

Question

One day, Captain Haddock receives a mysterious letter with a confusing paragraph. Captain Haddock and Tintin are investigating the matter. There are two possible suspects: Professor Calculus and Thomson $\&$ Thompson. Based on their past experience:
- The probability that Professor Calculus sends a letter is $60 \%$, while the probability that Thomson $\&$ Thompson send a letter is $40 \%$.

• When Professor Calculus sends letters, there is an $80 \%$ probability that the letter contains a confusing paragraph.
• When Thomson $\&$ Thompson send letters, there is a $5 \%$ probability that the letter contains a confusing paragraph.

What is the probability that the letter was sent by Professor Calculus?

• A. $0.96$
• B. $0.80$
• C. $0.50$
• D. $0.48$

   

Answer 1

P(C) = 0.6
P(T) = 0.4
P(con | C) = 0.8
P(con | T) = 0.05

Now, P(con) = P(con | C) * P(C) + P(con | T) * P(T) = 0.8*0.6 + 0.05*0.4 = 0.5
So, P(C | con) = P(con | C) * P(C) / P(con) = (0.8 x 0.6)/0.5 = 0.96

So, option A is correct.