Question

What is the difference between “The Probability of A and B” versus “The Probability of A or B”?

Answer 1

P(A and B) means the probability of the cases in which both events A and B occurs.

P(A or B) means the probability of the cases in which at least one of A or B occurs.

Consider tossing a die. Let A be the event that the outcome is less than 3

Let B be the event that the outcome is an even number.

A = {1,2}

B = {2,4,6}

A and B = {2}, because 2 is the only common element

A or B = {1,2,4,6}   (all elements in A or B are part of (A or B)}

P(A and B) = 1/6

P(A or B) = 4/6 = 2/3