Question

Use the general addition rule in context:

1. what is the probability that I either roll a 6 or a 3 when I roll a single die?

2. What is the probability that I draw a queen or a red card from a normal, 52-card deck?

please show math and explain i need to understand this

Answer 1

Here the two events are mutually exclusive P(3 or 6) = P(3) + P(6) For mutually exclusive events the probability that A or B occurs P(A or B) = P(A) + P(B) This Addition Rule 1 P(3 or 6) = P(3) + P(6) = 1/6 + 1/6 = 1/3 (2) Here the two events are non mutually exclusive Addition Rule 2 is applied. When two events are non-mutually exclusive the probability that A or B occurs is P(A or B) = P(A) + P(B) - P(A Intersection B) P(queen or red) = P(queen) + P(red) - P(queen or red) = 4/52 + 26/52 - 2/52 = 28/52 = 7/13 = 7/13