Sara-Grace P.
1 Expert Answer
William W. answered • 11/01/21
Math and science made easy - learn from a retired engineer
There are 12 total face cards in the deck, a Jack, Queen, and King of each of the four suits. And there are 52 total cards in the deck.
Draw #1: The probability of drawing a face card is 12/52 = 3/13
Draw #2: There are now only 11 face cards left in the deck and there are only 51 total cards so the probability of drawing a face card is 11/51.
The probability of BOTH events happening is the product of their individual probabilities:
3/13 • 11/51 = 33/663 = 11/221
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Two cards are drawn from a deck of cards. What is the probability that they are both face cards and at least one is red? Assume that there are $52$ cards and without replacement.
I have two different methods, and they got different solutions. The second method below is the same as the teacher's answer: $0.0385$, but the first is not. What is wrong with my first solution?
Method 1: $\frac{12\cdot11}{52\cdot51}\cdot\frac{3}{4}=0.0373$. I got this because I calculated the probability that I get two face cards, and then I multiplied by $\frac {3}{4}$ because there is $\frac {3}{4}$ chance that I get at least $1$ red.
Method 2: $\frac{\binom{12}{2}}{\binom{52}{2}}-\frac{\binom{6}{2}}{\binom{52}{2}}=0.0385$. The first fraction is the probability that both are face cards. The second fraction is the probability that they are both face cards and both black.
Selecting Cards Find the probability of getting 2 face cards (king, queen, or jack) when 2 cards are drawn from a deck without replacement. -------------------- There are 12 face cards. --- P(draw 2 face) = 12C2/52C2 = 0.0498.. ------------------------------------------ Cheers,
Stan H.