A single card is drawn at random from a standard 52- card deck. Find the probability of each event in fractions.
a. face card
b. face card or a 7
c. a face card or a spade
d. a face card, given that it is a spade
e. not a face card.
Michael
Favorite Answer
a. There are three types of face cards -- Jacks, Queens, and Kings. There are four of each, so 4 x 3 = 12. 12/52 = 3/13
b. Same as before, but now you have Jacks, Queens, Kings, and now sevens. Four choices, four of each, so 4 x 4 = 16. 16/52 = 4/13
c. Now you have two options which are not independent. There are 12 face cards P(FC)=12/52. (Probability of a face card= 12/52) and you have 13 spades. P(S)=13/52. But, you have an 'or'. To calculate an or probability, you add together the two options, and then subtract from it the probability of both situations happening simultaneously. This prevents you from double counting. In this situation, there are three face cards that are also spades so:
12/52 + 13/52 - 3/52 = 22/52 =11/26
d. Now....you know you have a spade, so what are the chances that the card you have is a face card. There are 13 spades. Three of them are face cards, so 3/13.
e. Not a face card is the exact opposite of item a. There are ten cards in the deck that aren't face cards --Ace through ten. Four each. 10 x 4 = 40 out of 52 cards. 40/52 = 10/13