If you are drawing one card from a regular deck of cards (52 cards

Question

If you are drawing one card from a regular deck of cards (52 cards, with 13 sets of four), what is the probability that you draw a 4 or a spade?

A. 4/13
B. 5/13
C. 7/13
D. 9/13
E. 11/13

IanStewart · Answer

We just need to count the number of cards that meet the conditions, and divide that number by 52, the total number of cards.

There are 13 spades in a deck, and there are 4 fours in a deck. But we've counted the four of spades twice, because that card belongs to both groups, so 13+4-1 = 16 cards meet our criteria, and the answer is 16/52 = 4/13.

King407 · Answer

P(A or B) = P(A) + P(B) - P(A&B)

P(A) = Drawing a 4; there are four 4's in a deck =>  \frac{4}{52}

P(B) = Drawing a spade; there are 13 spades in a deck =>  \frac{13}{52}

P(A&B) = Drawing a 4 of spade; there is one 4 of spade =>  \frac{1}{52}

Thus, P(A or B) =  \frac{4}{52} + \frac{13}{52} - \frac{1}{52} = \frac{16}{52} = \frac{4}{13}

Hence answer is  \frac{16}{52}  or  \frac{4}{13}

GMATinsight · Answer

Point 1: It would be nicer of us to post the question with the 5 options to make it look more relevant for GMAT as many questins in GMAT can be solved just by Option Elimination technique :lol:

Point 2: To solve questions of Cards one need to know that the pack of cards has 52 cards of 4 suits - 13 cards of Spade (Black in Color) - 13 cards of Clubs (Blackin Color) - 13 cards of Heart (Red in Color) - 13 cards of Diamond (Red in Color) Every Suit has cards from No.1(Ace) to Number 10 and then 1 Jack, 1 Queen and 1 King So total Spade = 13 cards Remaining No.4 cards = 4 (1 of each suit) -1(spade already counted) = 3 cards Total cards in the pack = 52 probability = Favorable Outcomes/ Total Coutcomes i.e. Probability = (13+3)/52 = 16/52 = 4/13

Nevernevergiveup · Answer

Thanks everyone for the solution. All are right in their approach. 
I just got confused in case of getting both a 4 and a spade (the 4 of spades).

Here is the solution
you should note that these two events are not mutually exclusive; you
could get both a 4 and a spade (the 4 of spades). So you must apply the general
case formula and remember to subtract the overlapping probability.
P(4) = 4/52= 1/13, 
P(Spades) = 13/52= 1/4, 
and P(4 and Spades) = 1/52.
P(4 or Spades) = 4/52+ 13/52− 1/52= 16/52= 4/13. 
The answer is 4/13.

bumpbot · Answer

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If you are drawing one card from a regular deck of cards (52 cards

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