## What is the probability that you get a pair when picking the top two cards off of a randomly shuffled deck of cards

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### What is the probability that you get a pair when picking the top two cards off of a randomly shuffled deck of cards

by AAPL » Tue May 09, 2023 11:46 am

00:00

A

B

C

D

E

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Veritas Prep

What is the probability that you get a pair when picking the top two cards off of a randomly shuffled deck of cards ($$52$$ cards, with $$13$$ sets of four matching suits)?

A. $$\dfrac{12}{2,652}$$

B. $$\dfrac{16}{2,652}$$

C. $$\dfrac{1}{17}$$

D. $$\dfrac{1}{13}$$

E. $$\dfrac{1}{2}$$

OA C

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### Re: What is the probability that you get a pair when picking the top two cards off of a randomly shuffled deck of cards

by Brent@GMATPrepNow » Mon May 15, 2023 6:09 am
AAPL wrote:
Tue May 09, 2023 11:46 am
Veritas Prep

What is the probability that you get a pair when picking the top two cards off of a randomly shuffled deck of cards ($$52$$ cards, with $$13$$ sets of four matching suits)?

A. $$\dfrac{12}{2,652}$$

B. $$\dfrac{16}{2,652}$$

C. $$\dfrac{1}{17}$$

D. $$\dfrac{1}{13}$$

E. $$\dfrac{1}{2}$$

OA C
P(select pair) = P(1st card is ANY card AND 2nd card matches 1st card)
= P(1st card is ANY card) x P(2nd card matches 1st card)
= 1 x 3/51
= 3/51
= 1/17
= C

Aside: P(2nd card matches 1st card) = 3/51, because once 1 card is selected, there are 51 cards remaining in the deck. Among those 51 remaining cards, there are 3 that match the 1st card selected.

Cheers,
Brent

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