Question

venn diagrams practice

1. a person is chosen at random from a group of friends. a is the event has blond hair and b is the event has blue eyes. the outcomes for outcomes a and b are shown in the venn diagram.

a) list the sample space.
list the set of outcomes for the following events:
b) has blond hair { }
c) does not have blond hair { }
d) has blue eyes { }
e) has blond hair and blue eyes { }
f) has blond hair but not blue eyes { }
g) has blue eyes but not blond hair { }
h) has neither blond hair nor blue eyes { }

1. find the following outcomes for the venn diagram drawn on the right:

a) the sample space s = { , , , , , , , } (outcomes inside the rectangle)
b) event a = { , , , }
c) event not a = { , , , , , }
d) event b = { , , , }
e) event not b = { , , , , , }
f) event a and b = { , }
g) event a or b = { , , , , , , }
h) event a or b but not both = { , , , }
i) event neither a or b = { , , , }

Explanation:

Step1: Identify sample space from Venn - diagram

The sample space is all the elements in the universal set (the rectangle in the Venn - diagram).

Step2: Identify events based on set - theory

For each event, we pick the relevant elements from the Venn - diagram. For example, for event A, we pick elements in circle A, for 'not A' we pick elements outside circle A, etc.

1.

Answer:

a) {Jen, Matt, Nick, Peter, Jack, Sue, Kate, Michael}
b) {Jen, Matt, Nick, Peter, Jack}
c) {Sue, Kate, Michael}
d) {Peter, Jack, Sue, Michael}
e) {Peter, Jack}
f) {Jen, Matt, Nick}
g) {Sue, Michael}
h) {Kate}

2.