Probability: Four cards are chosen from a deck...

[rama123]

Four cards are chosen from a standard deck of 52 playing cards with replacement.

What is the probability of getting 4 hearts?

A) 13/52
B) 1/16
C) 1/256
D) None of the above



EDITED!

[rama123]

Sorry,i got it,ans is 1/256.

[thefish]

One way of looking at it:

Pretend the deck only has 4 cards: 1 heart, 1 diamond, 1 spade, 1 club.

There are 4 * 4 * 4 * 4 = 256 possible hands. Only 1 of these hands has all 4 hearts. So it's 1/256.

[dkpbus]

Answer is 1/256 as correctly pointed out by thefish

with replacement everytime cards in pack would be 52 there are 13 cards of heart and everytime there will be 13 hearts so ans would be

13/52 * 13/52 *13/52 *13/52 = 1/256

Any Thought ?

[pankajagg]

aaahhh just a bit curious

suppose we have 52 cards , which are biased, now we draw 4 cards with replacement , what is the probability of all 52 cards being hearts ?

[diwakardiwa]

answer is '0'
because occurence of all the 52 cards being hearts will not occur, unless all the 52 cards are hearts only. Since the 52 cards contains 13 hearts, 13 spades, 13 clubs, 13 diamonds.
am i clear.

[diwakardiwa]

answer is '0'
because occurence of all the 52 cards being hearts will not occur, unless all the 52 cards are hearts only. Since the 52 cards contains 13 hearts, 13 spades, 13 clubs, 13 diamonds.
am i clear.

[pankajagg]

diwakardiwa these 52 cards are not the ordinary one ....they may contain all hearts. These 52 cards may contain 20 hearts and rest of the spadades ..etc etc

[vertical_horizon]

My solution:

The probability of getting 4 hearts = the number of ways we can get 4 hearts / the number of the ways we can get 4 arbitrary cards = m/n

Then, we have

m = (4,C,13), and n = (4,C,52).

The result is 11/4165.

The correct answer is (D).

Answer is 1/256 as correctly pointed out by thefish

with replacement everytime cards in pack would be 52 there are 13 cards of heart and everytime there will be 13 hearts so ans would be

13/52 * 13/52 *13/52 *13/52 = 1/256

Any Thought ?

--------------------------------------------------------------------------------
DKP

DKP. it must be:

The probability of choosing the first heart card: 13/52

The probability of choosing the second heart card: 12/51 (since there're only 12 hearts left out of 51 cards remained)

The probability of choosing the third heart card: 11/50 (since there're only 11 hearts left out of 50 cards remained)

The probability of choosing the forth heart card: 10/49 (since there're only 10 hearts left out of 49 cards remained)

The correct answer: 13/52 * 12/51 * 11/50 * 10/49 =11/4165

HTH !!!

phuong

[pankajagg]

m = (4,C,13), and n = (4,C,52) :o

The result is 11/4165.

52c4 will be used when cards are drawn togather

in this case deck is replenished as soon as one card is drawn

so probability is correctly pointed as 1/256