At an art group children are allowed to choose between four activities; colouring, painting, clay modelling and sketching.
There is a total of 60 children attending the art group. 12 of the boys chose the activity colouring.
A total of 20 children chose painting and a total of 15 chose clay modelling. 13 girls chose clay modelling.
8 of the 30 boys chose sketching, as did 4 of the girls.
Construct a two-way table to show this information.
Construct the table carefully, remember to include marginal totals for the rows and columns.
Work through each sentence in turn, placing a value in the table where possible and coming back later to a sentence if need be.
Once those values are in place, work your way around the rest of the table until it is complete.
If you find you can't complete the table, look back at the question for some information you may have missed.
Colouring | Painting | Clay modelling | Sketching | Total | |
Boys | 12 | 30 - 12 - 2 - 8 = 8 | 15 - 13 = 2 | 8 | 30 |
Girls | 30 - 12 - 13 - 4 = 1 | 20 - 8 = 12 | 13 | 4 | 60 - 30 = 30 |
Total | 12 + 1 = 13 | 20 | 15 | 8 + 4 = 12 | 60 |
So the final two-way table is
Colouring | Painting | Clay modelling | Sketching | Total | |
Boys | 12 | 8 | 2 | 8 | 30 |
Girls | 1 | 12 | 13 | 4 | 30 |
Total | 13 | 20 | 15 | 12 | 60 |
You can do a quick check of your table values by ensuring the marginal totals add up to the grand total.
Find the probability that a randomly selected child
chose colouring,
is a boy who chose sketching.
For this part of the question we are not interested in whether the child is a boy or a girl.
So we will need the values from the (marginal) total column for colouring, 13.
There are 60 children in total.
A girl is selected at random. Find the probability they chose the activity painting.
As we are only selecting from the girls, this will be "out of" 30 rather than the total of 60 that are in the group.
12 girls chose painting.