You have a sample space of 2 events called A and B. From your experimental observations you determine the probability of A or B {i.e. P(A or B)} to be 71%. You also conclusively determine that the probability of A is 30% and the joint probability of both events occurring is 19%. What is P(B)

Question

Eight people were asked how many immediate family members they have. The results were (5, 2, 4, 4, 3, 6, 7, 7). If one of the eight people were selected at random, what is the change of selecting an even number or less than 4

Answer 1

P(A∪B)=0.71
P(A)=0.3
P(A∩B)=0.19

The visual way to solve this problem is to draw a Venn diagram and fill in the respective probabilities.

If you prefer to solve it mathematically, use:
P(A∪B)=P(A)+P(B)-P(A∩B)

Answer 2

60