Question

TV Shows That I Haven't Seen Because I'm Too Busy Making HW Problems (15 points) As you may be aware, The Last Of Us and The Mandalorian are two of the more popular television shows these days. 96% of TV watchers like The Mandalorian. If someone likes The Mandalorian, there is an 93% chance they like The Last Of Us. If someone does not like the The Mandalorian, there is a 68% chance they like The Last Of Us. Let M be the event that a person likes The Mandalorian and L be the event that a person likes The Last Of Us.

(a) Describe in english what each of the following probabilities represent: (i) P(M), (ii) P(L∣M), (iii) P(M∣L
C ).
(b) Compute P(L). Show your work (the formulas and substitutions you made).
(c) Compute the probability that a student likes The Mandalorian, given that they like The Last Of Us. Show your work (the formulas and substitutions you made).

Answer 1

The question involves calculating conditional probabilities and the overall probability of liking two popular TV shows based on given probabilities.

Step-by-step explanation:

The student's question involves concepts of conditional probability and the computation of the overall probability of an event happening. The probabilities described in part (a) are: (i) P(M) represents the probability that a person likes The Mandalorian, (ii) P(L|M) represents the probability that a person likes The Last Of Us given they like The Mandalorian, and (iii) P(M|LC) is the probability that a person likes The Mandalorian given they do not like The Last Of Us. For part (b), P(L) can be computed using the Law of Total Probability. Finally, for part (c), the probability that a person likes The Mandalorian given they like The Last Of Us, denoted as P(M|L), requires the use of Bayes' theorem.