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stuck in prob again

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by quantskillsgmat » Sat Feb 25, 2012 9:23 pm
Q Laura has a deck of card with 13 of the 52 cards designated as heart. If she shuffles thouroughly and then deals 10 cards off the top of the deck, what is probability that 10th card dealt is a heart.
a)1/4 b)1/5 c)5/26 d)12/42 e)13/42

should it be 13/42 or 1/4.ans is 1/4
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by neerajkumar1_1 » Sat Feb 25, 2012 11:04 pm
probability whether the 10th card dealt is a heart will depend on whether any of the previous cards dealt were heart.
Probability that all other 9 cards were not heart and the 10th card is a heart = 13/52 = 1/4
Now when we consider the other possibilities, some additional fractions will be added to 1/4
Considering that, the decimal value should be greater than 0.25

Hence I would go for option E
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by GMATGuruNY » Sun Feb 26, 2012 5:00 am
quantskillsgmat wrote:Q Laura has a deck of card with 13 of the 52 cards designated as heart. If she shuffles thouroughly and then deals 10 cards off the top of the deck, what is probability that 10th card dealt is a heart.
a)1/4 b)1/5 c)5/26 d)12/42 e)13/42

should it be 13/42 or 1/4.ans is 1/4
P(heart on the Nth pick) = P(heart on the FIRST pick).

In other words, the probability of selecting a heart ON ANY GIVEN PICK is equal to the probability of selecting a heart on the FIRST PICK:
P(heart on ANY GIVEN PICK) = P(heart on the first pick) = 13/52 = 1/4.

Thus:
P(heart on the SECOND pick) = 1/4.
P(heart on the THIRD pick) = 1/4.
P(heart on the FOURTH pick) = 1/4.
And so on.

Thus, P(heart on the TENTH pick) = 1/4.

The correct answer is A.

For more on this concept, check my posts here:

https://www.beatthegmat.com/probablity-ques-t60161.html

https://www.beatthegmat.com/manhattan-pr ... 89481.html

https://www.beatthegmat.com/probability-t60530.html
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by Mr.Hollywood » Mon Feb 27, 2012 9:43 pm
GMATGuruNY wrote:
quantskillsgmat wrote:Q Laura has a deck of card with 13 of the 52 cards designated as heart. If she shuffles thouroughly and then deals 10 cards off the top of the deck, what is probability that 10th card dealt is a heart.
a)1/4 b)1/5 c)5/26 d)12/42 e)13/42

should it be 13/42 or 1/4.ans is 1/4
P(heart on the Nth pick) = P(heart on the FIRST pick).

In other words, the probability of selecting a heart ON ANY GIVEN PICK is equal to the probability of selecting a heart on the FIRST PICK:
P(heart on ANY GIVEN PICK) = P(heart on the first pick) = 13/52 = 1/4.

Thus:
P(heart on the SECOND pick) = 1/4.
P(heart on the THIRD pick) = 1/4.
P(heart on the FOURTH pick) = 1/4.
And so on.

Thus, P(heart on the TENTH pick) = 1/4.

The correct answer is A.

For more on this concept, check my posts here:

https://www.beatthegmat.com/probablity-ques-t60161.html

https://www.beatthegmat.com/manhattan-pr ... 89481.html

https://www.beatthegmat.com/probability-t60530.html
Seems like the following question can also be fallen under the umbrella of the Golden Rule. Or can it?

A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer?
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