Question

You randomly survey students about whether they are in favor of planting a community garden at school. Of 96 boys surveyed, 61 are in favor. Of 88 girls surveyed, 17 are against. Organize the results in a two-way table. What is the probability of randomly choosing a student that is against the garden and is a girl?
Please show all work I’m lost on this, thank you!

Answer 1

         boys           girls

yes    61               71

no     35               17

In order to find out how many boys are against you do 96 - 61. In order to find out how many girls are in favor you do 88 - 17.

In order to find the probability  you make a proportion. It will be:

$\frac{number of girls against}{total number of students} = \frac{p}{100}$

So plug in you numbers.

$\frac{17}{184} = \frac{p}{100}$

Then you solve the proportion using cross multiplication.

$17 * 100 = 184p$

$1700 = 184p$

$\frac{1700}{184} = \frac{184}{184}p$

$9.23913043478 = p$

So, the chance of randomly picking a girl that's against the garden is 9.23913043478%