Question

There are 9 movies ranked on the summer's "must see movie list." What is the probability that you guess the summer's top two must see movies if you randomly guess?

Answer 1

Answer:

1/36 = 0.0278 = 2.78% probability that you guess the summer's top two must see movies if you randomly guess

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, the order in which the movies are chosen is not important, which means that we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Desired outcomes:

Top two movies, so only one outcome, which means that $D = 1$

Total outcomes:

Two movies from a set of 1. So

$T = C_{9,2} = \frac{9!}{2!(9-2)!} = 36$

Probability:

$p = \frac{D}{T} = \frac{1}{36} = 0.0278$

1/36 = 0.0278 = 2.78% probability that you guess the summer's top two must see movies if you randomly guess