Venn Diagram and Probability Tutorial

Consider the following sets

A={0.2,0.2,0.1,0.07} B={0.05,0.05,0.01,0.03} C={0.2,0.06} In Venn diagram,the sets A,B,C are represented as

Calculation of P(A)

Probability of A is represented as P(A) P(A) is calculated by adding all values of the set A. P(A)=0.2+0.2+0.1+0.07=0.57 In venn diagram, P(A) is pictorially represented as

Calculation of P(B)

Probability of B is represented as P(B) P(B) is calculated by adding all values of the set B. P(B)=0.05+0.05+0.01+0.03=0.14 In venn diagram, P(B) is pictorially represented as

Calculation of P(AUB)

Probability of AUB is represented as P(AUB) P(AUB)=P(A)+P(B)=0.57+0.14=0.71 In venn diagram, P(AUB) is pictorially represented as

Calculation of P(A∩B)

Probability of A∩B is represented as P(A∩B) P(A∩B)=0.2+0.06=0.26 In venn diagram, P(A∩B) is pictorially represented as

Calculation of P(A^c)

Probability of A^c is represented as P(A^c) P(A^c)=1-P(A)=1-0.57=0.43 In venn diagram, P(A^c) is pictorially represented as

Calculation of P(B^c)

Probability of B^c is represented as P(B^c) P(B^c)=1-P(B)=1-0.14=0.86 In venn diagram, P(B^c) is pictorially represented as

Calculation of P(AUB)^c

Probability of AUB^c is represented as P(AUB)^c P(AUB)^c=1-P(AUB)=1-0.71=0.29

Calculation of P(A∩B)^c

Probability of A∩B^c is represented as P(A∩B)^c P(A∩B)^c=1-P(A∩B)=1-0.26=0.74 In venn diagram, P(A∩B)^c is pictorially represented as

Calculation of P(A^c∩B^c)^c

Probability of (A^c∩B^c)^c is represented as P(A^c∩B^c)^c P(A^c∩B^c)^c=1-P(A)-P(B)+P(A∩B)=1-0.57-0.14+0.26=0.55