Probability of A or B (2 of 3)
The only way in which an ace and a spade can both be drawn is to draw the ace of spades. There is only one ace of spades, so:
p(ace and spade) = 1/52 .
The probability of an ace or a spade can be computed as:
p(ace)+p(spade)-p(ace and spade) =
4/52 + 13/52 - 1/52 = 16/52 = 4/13.
Consider the probability of rolling a die twice and getting a 6 on at least one of the rolls. The events are defined in the following way:
Event A: 6 on the first roll:
p(A) = 1/6
Event B: 6 on the second roll:
p(B) = 1/6
p(A and B)
= 1/6 x 1/6
p(A or B) = 1/6 + 1/6 - 1/6 x 1/6 = 11/36
The same answer can be computed using the following admittedly convoluted approach:
Getting a 6 on either roll is the same thing as not getting a number from 1 to 5 on both rolls. This is equal to:
1 - p(1 to 5 on both rolls).