Some of the children at a school arrive by car.

30% of the children at the school are boys

60% of the boys at the school arrive by car

80% of the girls at the school arrive by car

what is the probability that a child chosen at random from the school arrives by car? give your answer as a decimal

74%

Explanation:

You can build a two-way relative frequency table to represent the dа ta:

These are the columns and rows:

Car No car Total

Boys

Girl

Total

Fill the table

30% of the children at the school are boys

Car No car Total

Boys 30%

Girl

Total

60% of the boys at the school arrive by car

That is 60% of 30% = 0.6 * 30% = 18%

Car No car Total

Boys 18% 30%

Girls

Total

By difference you can fill the cell of Boy and No car: 30% - 18% = 12%

Car No car Total

Boy 18% 12% 30%

Girl

Total

Also, you know that the grand total is 100%

Car No car Total

Boy 18% 12% 30%

Girl

Total 100%

By difference you fill the total of Girls: 100% - 30% = 70%

Car No car Total

Boy 18% 12% 30%

Girl 70%

Total 100%

80% of the girls at the school arrive by car

That is 80% of 70% = 0.8 * 70% = 56%

Car No car Total

Boy 18% 12% 30%

Girl 56% 70%

Total 100%

Now you can finish filling in the whole table calculating the differences:

Car No car Total

Boy 18% 12% 30%

Girl 56% 14% 70%

Total 74% 26% 100%

Having the table completed you can find any relevant probability.

The probability that a child chosen at random from the school arrives by car is the total of the column Car: 74%.

That is because that column represents the percent of boys and girls that that arrive by car: 18% of the boys, 56% of the girls, and 74% of all the the children.