As part of a study done for a large corporation, psychologists asked randomly selected employees to solve a collection of simple puzzles while listening to soothing music. twenty-three (23) out of 56 employees solved the puzzles in less than 7 minutes. suppose an employee in the study is selected randomly. calculate the probability that they take longer than 7 minutes to solve the puzzles.

And that represent the probability that they take longer than 7 minutes to solve the puzzles.

Step-by-step explanation:

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by:

On this case we have that n= 56 represent the employees selected to solve the puzzles.

We know that 23 out of the 56 selected solved the puzzles in less than 7 minutes.

Let's define the events A and A' like this:

A: Employees solved puzzles in less than 7 minutes

By the complement rule then:

A' : Employees solved puzzles in more than 7 minutes

Based on this we are interested to find the probability for A'

We can begin finding P(A), from the definition of probability we know:

For this case if we replace we got:

And using the complemnt rule we got:

And solving for P(A') we got:

And that represent the probability that they take longer than 7 minutes to solve the puzzles.

c. (3,2,6) is the answer.