Question

Kate and Jenny are about to watch 2 movies. There are 25 movies in Jenny's collection and she suggests that they are going to choose the movies at random. Kate decides (secretly) that she has chosen her 2 favorites.

Step 1 of 2: What is the probability that Kate's top 2 will be the 2 selected? Express your answer as a simplified fraction.

Step 2 of 2: Suppose the movies Kate has chosen also are meant to be viewed in a particular order. What is the probability that the films are chosen in the correct order with the random drawing process? Express your answer as a simplified fraction

Answer 1

Step 1:

Number of ways of selection in which 2 movies can be selected out of 25 movies = 25C2 = 300

Number of ways of selection in which the 2 movies selected are the Kate's top 2 movies = 2C2 = 1

Thus, the required probability = 1/300

Step 2:

Probability that the first film chosen by Kate is the same as the first chosen movie at random = 1/25

and probability that the second film chosen by Kate is the same as the second chosen movie at random provided the first movie was same = 1/24

Thus, the required probability = 1/25 * 1/24 = 1/600