What is the Probability of Getting Two Cards that Belong to the Same GMAT Problem Solving

Question: What is the probability of getting two cards that belong to the same color when two cars are drawn at random from a pack of 52 cards?

A. \(1\over 2\)
B. \(25\over 51\)
C. \(\frac{^{26}C_2}{^{52}C_2}\)
D. \(1\over 26\)
E. \(25\over 52\)

Answer:
Approach Solution (1):
In a pack of 52 cards, there are 26 black cards (13 spade and 13 club), and 26 red cards (13 heart and 13 diamond)
Now, the probability of selecting 1st card from 52 cards: 1;
Remaining cards of same colors = 25;
Total remaining cards = 51;
So, the probability of selecting 2nd card of same color =\({1\over51}*25={25\over51}\)
Correct option: B

Approach Solution (2):
Total number of ways =\({^{52}C_2} \)
Selecting both red cards =\({^{26}C_2}\)
Selecting both black cards =\({^{26}C_2}\)
Probability =\({{2*{^{26}C_2}}\over{^{52}C_2}}={25\over51}\)

Correct option: B

Approach Solution (3):
We must assume that half of the cards are red and half are black
The probability of getting two red cards =\({26\over52}*{25\over51}={1\over2}*{25\over51}={25\over102}\)
Since the number of black cards is same as the number of reds, the probability of selecting two black cards is also\(25\over102\)
So probability of selecting two cards of the same color (either both are red or both are black) is\({25\over102}+{25\over102}={50\over102}={25\over51}\)

Correct option: B

“What is the probability of getting two cards that belong to the same color when two cars are drawn at random from a pack of 52 cards?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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