Question

Merry doesn't watch very many movies. When she gets to pick what she and her friends do, she never picks going to a movie. So whenever she does watch a movie, it's always something someone else picked and she doesn't like it very much.

Of all movies, both the ones she's Seen and the ones she Hasn't, there's only a 10% chance that she Likes the movie.

However, she's less likely to See movies she Likes. The probability she Sees a movie that she Likes is 5%, while the probability she Sees a movies that she Doesn't Like is 15%.

It's saturday night and her friends have decided they're all going to watch a movie on Zoom together. Given that this is a movie she is going to See, what's the probability she Likes it?

Answer 1

Given ,

P( Merry likes a movie ) = 0.10

P(Merry watches a movie I Merry likes the movie) =0.05

P(Merry watches a movie I Merry does not like the movie) =0.15

To find P( Marry likes the movie I Marry watches the movie)

Using Bayes theorem

P( Marry likes the movie I Marry watches the movie)

= P(  Marry watches the movie I  Merry likes the movie) *P(Merry likes the movie) /P( Marry watches the movie)

Now

P( Marry watches the movie) = P(Merry watches a movie I Merry likes the movie) *P(Merry likes the movie)

+ P(Merry watches a movie I Merry does not like the movie) *P(Merry does not like the movie)

= 0.05*0.10 + 0.15* (1-0.10)

= 0.005 + 0.135

= 0.14

Therefore ,

P( Marry likes the movie I Marry watches the movie)

= 0.05*0.10 / 0.14

= 0.0357

Probability that Merry likes the movie given that she is going to see the movie = 0.0357