Romain knows the following information about the 32 3232 classes he took in high school: He studied for but did not pass 3 33 classes. He passed 27 2727 classes in total. He studied for 26 2626 classes in total. Can you help Romain organize the results into a two-way frequency table?

The two-way frequency table is shown below.

Step-by-step explanation:

Romain took a total of N = 32 classes in high school.

Denote the events as follows:

X = Romain studied for a class

Y = Romain did not studied for a class

A = Romain passed the class

B = Romain did not pass the class

The information provided is:

n (X ∩ B) = 3

n (A) = 27

n (X) = 26

Compute the number of classes Romain did not pass as follows:

n (B) = N - n (A)

       = 32 - 27

       = 5

Compute the number of classes Romain did not study for as follows:

n (Y) = N - n (X)

       = 32 - 26

       = 6

Compute the number of classes Romain did not study for and did not pass as follows:

n (Y ∩ B) = n (B) - n (X ∩ B)

               = 5 - 3

               = 2

Compute the number of classes Romain did not study for but passed as follows:

n (Y ∩ A) = n (Y) - n (Y ∩ B)

               = 6 - 2

               = 4

Compute the number of classes Romain did study for and passed as follows:

n (X ∩ A) = n (A) - n (X ∩ A)

               = 27 - 4

               = 23

The two-way frequency table is as follows:

                                   Studied (X)     Did not Studied (Y)     Total

            Passed (A):           23                         4                        27

Did not Passed (B):            3                         2                          6

                     Total:           26                         6                        32

y > 1/3x

y < = -x + 4

hope this : )

24

step-by-step explanation: