venn diagrams practice\n1. a person is chosen at random from a group of friends. a is the event has blond…

venn diagrams practice\n1. 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.\n a) list the sample space.\nlist the set of outcomes for the following events:\n b) has blond hair { }\n c) does not have blond hair { }\n d) has blue eyes { }\n e) has blond hair and blue eyes { }\n f) has blond hair but not blue eyes { }\n g) has blue eyes but not blond hair { }\n h) has neither blond hair nor blue eyes { }\n2. find the following outcomes for the venn diagram drawn on the right:\n a) the sample space s = { , , , , , , , } (outcomes inside the rectangle)\n b) event a = { , , , }\n c) event not a = { , , , , , }\n d) event b = { , , , }\n e) event not b = { , , , , , }\n f) event a and b = { , }\n g) event a or b = { , , , , , , }\n h) event a or b but not both = { , , , }\n i) event neither a or b = { , , , }

venn diagrams practice\n1. 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.\n a) list the sample space.\nlist the set of outcomes for the following events:\n b) has blond hair { }\n c) does not have blond hair { }\n d) has blue eyes { }\n e) has blond hair and blue eyes { }\n f) has blond hair but not blue eyes { }\n g) has blue eyes but not blond hair { }\n h) has neither blond hair nor blue eyes { }\n2. find the following outcomes for the venn diagram drawn on the right:\n a) the sample space s = { , , , , , , , } (outcomes inside the rectangle)\n b) event a = { , , , }\n c) event not a = { , , , , , }\n d) event b = { , , , }\n e) event not b = { , , , , , }\n f) event a and b = { , }\n g) event a or b = { , , , , , , }\n h) event a or b but not both = { , , , }\n i) event neither a or b = { , , , }

Answer

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.

Answer:

a) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} b) {2, 4, 6, 8} c) {0, 1, 3, 5, 7, 9} d) {6, 7, 8, 9} e) {0, 1, 2, 3, 4, 5} f) {2, 4} g) {0, 1, 2, 3, 4, 5, 6, 8} h) {2, 4, 7, 9} i) {0, 1, 3, 5}