Answer to Question #221238 in Combinatorics | Number Theory for Tasha

Question

20 trucks were tested at a check point. 6 trucks failed the test for brakes. 7 trucks failed the test for light. 9 trucks passed the tests for both brakes and lights
A) complete the Venn diagram
B) find n(B'nL')

Answer 1

A)

B}

$$n(U)=20$$

$$n(B'\cap L')=9$$

$$n(B\cup L)=20-9=11$$

$$n(B)=6, n(L)=7$$

$$n(B\cup L)=n(B)+n(L)-n(B\cap L)$$

$$n(B\cap L)=6+7-11=2$$