SOLUTION: If 2 cards are selected from a standard deck of 52 cards without replacement, find these probabilities. a. Both are spades. b. Both are the same suit. c. Both are kings.

Algebra ->  Probability-and-statistics -> SOLUTION: If 2 cards are selected from a standard deck of 52 cards without replacement, find these probabilities. a. Both are spades. b. Both are the same suit. c. Both are kings.      Log On


   

Question 395418: If 2 cards are selected from a standard deck of 52 cards without replacement, find these probabilities.
a. Both are spades.
b. Both are the same suit.

c. Both are kings.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you started.

a)

There are 13 spades out of 52 cards total. So P(drawing spade on first draw) = 13/52

After the first draw, there are 12 spades out of 51 total. So P(drawing spade on second draw) = 12/51. Remember, we're NOT replacing the cards.


So P(Both Spades) = P(drawing spade on first draw)*P(drawing spade on second draw)=(13/52)(12/51) = 156/2652 = 1/17


So the probability is 1/17
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b)

Regardless of what suit is chosen on the first draw, we'll have 12 cards left over in that selected suit (since all 4 suits have 13 cards) out of 51 total


So P(Both same suit) = 12/51


Note: the first card does not matter because the second card determines the entire probability. If you're still unsure, do some simulations (ie actually pull out a deck of cards and start drawing). Say on the first draw you pick a heart (actual face value doesn't matter). You'll then have 12 heart cards left out of 51 cards total.


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c)

I leave this one for you to try. Let me know if you still need help.