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 (\(52\) 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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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.

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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