Jonas knows the following information about the 19 members in his travel group:

•5 members have been to both the United States and Australia,

•11 members in total have been to the United States.

• 12 members in total have been to Australia,

Can you help Jonas organize the results into a two-way frequency table?

Have been to the US and Australia.

Haven’t been to the US but have been to Australia.

Haven’t been to Australia but have have US.

Haven’t been to both.

The complete two-way frequency table is shown below.

Step-by-step explanation:

Denote the events as follows:

U = a member have been to the United States

NU = a member have not been to the United States

A = a member have been to Australia

NA = a member have not been to Australia

The information provided is:

              A         NA        Total

 U          5          __           11

NU       __         __           __    

Total      12         __           19

Complete the table as follows:

n (U ∩ NA) = n (U) - n (U ∩ A)

                 = 11 - 5

                 = 6

n (NU) = N - n (U)

          = 19 - 11

          = 8

n (NU ∩ A) = n (A) - n (U ∩ A)

                 = 12 - 5

                 = 7

n (NA) = N - n (A)

          = 19 - 12

          = 7

n (NU ∩ NA) = n (NA) + n (U ∩ NA)

                     = 7 - 6

                     = 1

The complete 2-way table is:

              A         NA        Total

 U          5           6           11

NU        7            1           8    

Total      12          7           19

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