Question

Six cards are randomly distributed from a standard pack of 52 playing cards. Determine the probability that exactly one of the 6 cards is a queen.

Answer 1

so How many queen you have in deck ??

Answer 2

4

Answer 3

so, 6 cards out of 52 = 52C6

what it would be ?

Answer 4

and for a queen out of 6 cards, chances are 6C4 = ??

Answer 5

do not simplify much... just right a ratio..

Answer 6

wait but why are the chances for a queen out of 6 cards 6C4? shouldn't the chances be higher?

Answer 7

we have picked 6 cards from the deck.. and one of them should be queen.. as we have only 4 queen .. the combination would be 6C4...

Answer 8

why not 6C1?

Answer 9

oh, i guess m wrong.. it can be 4C1...

wait, m confused.. hold on..

Answer 10

ok, lets start again..

You pick 6 cards from a deck, so that would be 6/52

and one of them should be queen, for that its is 1/4

So the probability of event - 6/52 * 1/4 = 3/104...

is this the answer ??

Answer 11

the answer for ur working is 0.0288 but the textbook answer 0.336

Answer 12

sorry, I got to go but please type the solution if u get it.

Answer 13

queen can come exactly in one place.
remaining 5 places must have to be filled by other 48 cards

Answer 14

number of ways of drawing queen for one place = 4C1
number of ways of drawing remaining 5 cards = 48C5

total number of ways of drawing 6 cards = 52C6

Answer 15

probability of having exactly one queen = \( \frac{4C1 * 48C5}{52C6} \)

Answer 16

@ganeshie8 : amazing man.. i made same mistake as yesterday... thank u man !! :)

Answer 17

welcome yaar.. .ty :)

Answer 18

wait @ganeshie8 why is it 4C1, why is the n only equal to 4 shouldn't it be more?

Answer 19

you have only 4 queens in the deck.
and you want to choose 1

so its 4C1

Answer 20

so u don't use anything given in the question basically then?

Answer 21

i didnt get u

Answer 22

for that part

Answer 23

4C1

Answer 24

you have used the "1" thing given in the question

Answer 25

question says to choose only "1" queen

Answer 26

but why isn't it 6C1?

Answer 27

6C1 is : drawing one queen from 6 queens

Answer 28

yeh I don't know

Answer 29

I'm just trying to connect all of it together

Answer 30

dunno, I'm lost but I understand what you did.

Answer 31

don't worry, I think I got it now.

Answer 32

think of it like this,

1) First, you pick 1 queen from the available 4 queens - since its a combination, it doesnt matter which place you put in

Answer 33

sorry, I have to do stuff, so afk.

Answer 34

its ok... glad to hear u get it :D

Answer 35

but thanks for having the patience to help me.

Answer 36

u really deserve more than a medal.

Answer 37

np