Problem 2 [13 marks A box with movie recommendations has 3 romantic comedy title

Question

Problem 2 [13 marks A box with movie recommendations has 3 romantic comedy titles, 2 horror titles, and 3 action titles. A title is randomly selected. It is then placed back in the box, with an additional (different) recommendation from the same genre. For example, if Joel randomly selects a horror movie title, he will place the selected movie back in the box, and add his own recommended horror movie. Note: Read the assignment instructions Remember to define your events clearly, use proper notation, show all work, and include ain interpretative statement for contertual problems! a) (7 marks) What is the probability that the second selected movie is an action film? b) (4 marks) What is the probability that the first selected movie was a romantic comedy, if the second selected movie is an action film? c) (2 marks) What is the probability the second movie is a horror film if the first selected movie was a romantic comedy?

Explanation / Answer

There are 3 romcom, 2 horrow, 3 action movie titles. Pickeup up titles will be replaced with same genre movie title

a. P( 2nd movie is action movie) = ?

This will also depend whether 1st movie was action or not. So,

P( 2nd movie is action movie) = P( 1st is action)*P( action in 2nd) + P( 1st is not action)*P(action in 2nd)

= (3/8)*(3/8) + (5/8)*(3/8)

= 0.375

b. P( first is romantic ccmedy if 2nd is action) = (3/8)*(3/8)/((3/8)*(3/8) + (5/8)*(3/8))= 3/8 = .375

c. P( horror in 2nd given we get romcom in 1st) = P(romcom in 1st)*P(horror in 2nd) = (3/8)*(2/8) = 0.09375

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