Aces

Probability Level 2

You get from a deck of cards the four aces. You put these cards in a table and these cards are facing down. You have 2 red cards (Heart and Diamond) and 2 black cards (Club and Spade). What is the probability to choose two cards at random, and each card be of different colors?

\frac{5}{2}

\frac{1}{2}

\frac{2}{3}

\frac{3}{5}

4 solutions

Daniel Liu
Jul 22, 2014

First, pick any random card. Then, there are $2$ cards left with opposite colors out of the $3$ cards left in total; thus, the answer is $\boxed{\dfrac{2}{3}}$ .

I think the solution should be like this: There are two ways to choose a color(2) Out of four the first card could be anything.Hence prob is 1 and the 2nd card should be of the same color as the first(hence prob is 1/3)

Hence the prob that two cards are of same color would be 2 (1 1/3)= 2/3

Sriram Sitharaman - 6 years, 10 months ago

Tanuj Rohatgi
Aug 4, 2014

We have 4 cards - 2 black and 2 red , Then in 2C1 way we can pick one black card.. Similarly in 2C1 way we can pick a red card . Since we need to pick in total two cards the sample space is 4C2.. Therefore Probability = {2C1 X 2C1}/4C2= 4/6 = 2/3

Vaibhav Borale
Jul 24, 2014

Solution

Sriram Sitharaman
Jul 23, 2014

Aces

4 solutions

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