Question

An investigation of a number of automobile accidents revealed the following information:15 accidents involved alcohol and excessive speed27 accidents involved alcohol.13 accidents involved excessive speed but not alcohol22 accidents involved neither alcohol nor excessive speedHow many accidents were investigated? ** note: Let the universal set U be the set of all automobile accidents. Use the information provided to create a Venn diagram containing 2 subsets. Let A be the set of accidents involving alcohol and S be the set of accidents involving excessive speed. **

Answer 1

To solve this type of question we should use the Venn diagram

Let me draw it and show you where we will put each number given

Since there are 15 accidents involved alcohol and excessive speed

Then we should put 15 in the common part of the 2 circles

Since there are 27 accidents involved alcohol

That means 27 = alcohol only + alcohol and excessive speed

Then to find alcohol only we should subtract 15 from 27 to get the number of alcohol only

27 - 15 = 12

Since there are 13 accidents involved excessive speed but not alcohol

That means the excessive speed only is 13

Let us put it in the Venn diagram

Since there are 22 accidents involved neither alcohol nor excessive speed

That means we will put this number outside the circles inside the rectangle

To find the total number of accidents we will add all the numbers in the figure

`\begin{gathered} T_(acc)=12+15+13+22 \\ T_(acc)=62 \end{gathered}`

Then there are 62 accidents in this investigated