A random card is selected from a well-shuffled deck. What is the probability that a face card or a spade is selected?
a) Which formula, the addition rule or the multiplication rule, would be used to calculate the probability? Explain why.
You would use the addition rule for this problem, which is P(A U B) = P(A) + P(B) - P(AB).
In this problem, there are 12 total face cards in a deck (consisting of Jacks, Queens, and Kings) and there are 13 spade cards in a deck. However, 3 of the spades have already been accounted for in the 12 face cards, which then leaves 10 non-face spade cards. You would want to use the addition rule so that those cards aren't double-counted, which would result in the wrong probability being calculated.
b) Use the rule from part a to calculate this probability.
A = event of drawing a face card
B = event of drawing a spade
P(A U B) = P(A) + P(B) - P(AB)
= 12/52 + 13/52 - 3/52
= 22/52 = 0.42307692
So the probability of picking a face or spade card is about 42.30%.