On the first day of Christmas, Calvin gave to me

A Partridge in a Pear Tree.

From a deck of 52 cards, you draw 2 cards (without replacement). Given that the first card is a 3, what is the probability that you get a pair of threes (pear tree)?

(1) 1 221 \frac{1}{221}
(2) 4 52 \frac{4}{52}
(3) 3 51 \frac{3}{51}
(4) 13 52 \frac{13}{52}

1 3 2 4

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6 solutions

Daniel Liu
Dec 20, 2013

There are 3 "three's" left, and 51 cards left. Therefore the probability is 3 51 \boxed{\frac{3}{51}} .

Even though I got it right I don't UNDERSTAND the meaning of "pear trees" at LAST.!!

:(

Arya Samanta - 7 years, 1 month ago

In the deck of 52 cards, there are four 3s.

Since one 3 has been taken without replacement, three 3s are left in a deck of 51 cards.

Hence the probability 3 51 \frac{3}{51} .

Pavithra Pavi
Dec 22, 2013

Total cards 52. Already one card draw balance cards 51.Next get a pair of three cards so the probability is 3/51

A standart 52 cards deck has 4 card of each rank (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, King, Queen and Jack), one per suit (club, diamond, heart and spade). You draw two cards, one of them being a 3. Since there are 52 cards in a deck, after you draw one there will remain 51 cards, and between those there are still 3 cards rank 3. Thus, the probability of drawing another 3 is of 3 51 \frac{3}{51} .

thatz the best!!

Viraj Mohile - 7 years, 5 months ago

Thanks a lot! :D

José Robson Júnior - 7 years, 5 months ago
Prasun Biswas
Dec 21, 2013

It is given that out of the 2 cards drawn, one is a 3, so we have to find the probability of getting another 3 from the remaining 51 cards. Since, there are four 3's in a deck and one is already taken for the pair, there are three 3's remaining in the deck.

So, probability of getting a pair = 3 51 = \boxed{\frac{3}{51}}

Nicely written.

YASH KASAT - 7 years, 5 months ago

As you get that card the total number of cards deduct and its probability would decrease

Em um baralho temos um total de 52 cartas. Elas são divididas em 4 grupos sendo que em cada grupo as cartas com números vão de 2 a 10. Como já foi tirada uma carta nos restam apenas 51 cartas no total e 3 cartas com o número 3. Logo a probabilidade é 3 51 \frac{3}{51}

Marcos Oliveira - 7 years, 5 months ago

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