M4maths Previous Puzzles

13 Jul 2011 Find the probability

In a pack of 52 cards, 3 cards are drawn at random. What will be the probability to get an ace & two kings

OPtion

1) 6/(13*17*25)
2) 7/(13*16*25)
3) 4/(12*13*23)
4) 6/(12*17*25)
5) 5/(3*7*25)
6) 6/(13*25*25)
7) 6/(3*17*25)
8) 3/(6*23*25)
9) 3/(6*5*7)
10) none of these

Solution

Required Probability = [{(4*3)/(2*1)}*{(4/1)}*{(3*2*1)/(2*1)}]/[{(52*51*50)/(3*2*1)}]

OR

(4C2*4C1*3!/2!)/(52C3)

By solving

6/13*17*25

Correct Option: 1 Best Solution (7)

abhilash   13 years AGO

we need to draw 3 cards from 52 cards. so, the probability to select 3 cards is 52c3=(52*51*50)/(3*2*1).
And we need to draw one ace and two kings.so, the probability to drawing one ace and two kings from 4 cards of ace and 4 cards of kings is
4c1(4)* 4c2((4*3)/(2*1))/((52*51*50)/(3*2*1)=
6/(13*17*25)

Like? Yes (6) | No   

sowmya   13 years AGO

(4c1*4c2)/52c3=>6/(13*17*25)
so,option 1

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Aparajita Chowdhury   13 years AGO

we can choose 3 cards 52c3 ways.so,p(S)=26*17*50
by choosing 1 ace and 2 kings is:- p(E)=4c1 * 4c2
that means,p(E)=4 * 6
therefore,p(E)/p(S)=4*6/26*17*50=6/13*17*25

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swetha   13 years AGO

from the pack of 53 cards 3 are selected so that
the total probability of selecting 3 among 52 is 52c3
there are 4 ace cards and 4 kings in the pack of cards
probability of selecting 1 ace and 2 kings from pack of 52 is 4c1*4c2/52c3=6/13*17*25

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monika racharla   13 years AGO

4 aces and 4 kings are presnt out of 52 cards.

select (4c1*4c2)/52c3=6/(13*17*25)

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Ranjeet Verma   13 years AGO

(4C1*4C2)/52C3
=6/(13*17*25)

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dharmil   13 years AGO

selecting an ace from pack of cards is 4C1.
selecting two kings from pack of cards is 4C2.
so probability of selecting 3 cards from pack of cards which is an ace and 2 kings is
4C1*4C2/52C3.
on simplification=6/(13*17*25).

Like? Yes (2) | No