Question

Probability:

A card is drawn from a pack. The card is replaced and the pack is reshuffled. If this is done six times , the probability that 2 hearts, 2 diamonds and 2 black cards are drawn is. 90/2^(10)

I am unable to get the result. Please help !!!

Answer 1

@ganeshie8

Answer 2

So the result is supposed* to be this?\[\left(\frac{90}{2}\right)^{10}\]

Answer 3

90/(2^(10))

Answer 4

probability of a heart being drawn in 1 draw = 1/4
for a diamond = 1/4
for a black card = 1/2

probability of drawing HHDDBB = 1/4 * 1/4 *1/4*1/4*1/2*1/2= 1 / 1024

Answer 5

which is 1 / 2^10

Answer 6

Sorry, my internet lagged out.

So this?\[\left(\frac{90}{2^{10}}\right)\]

Answer 7

- but this result is just for the given order The order of drawing could be HHBDBD for example

Answer 8

yes it is @kittiwitti1

Answer 9

Okay.
Well, I would try to help but @welshfella seems to be helping you already, so I'll just go... ; w;

Answer 10

so we need to work out how many different arrangements of the cards are possible - and hope its 90!

Answer 11

90! is an astronomical number =P

Answer 12

I think its 6! / 2^3

Answer 13

6! / 2! 2! 2!

Answer 14

- if my memory of this stuff serves me well..

Answer 15

6C2*4C2*2C2*1/4 * 1/4 *1/4*1/4*1/2*1/2=90/(2^10)

will it be like this. Cause for 2 hearts to obtain of 6 cards is 6C2 and from the rest 4 we need 2 diamonds and 2 black cards obtained at the last.

Answer 16

= 720/8 = 90

Answer 17

6C2 * 4C2 * 2C2 =90

Answer 18

both will work, bt welshfella's method looks a lot simpler

Answer 19

yes - your method is valid @praxer

Answer 20

`HHDDBB`

possible permutations = 6!/(2!2!2!)

Answer 21

lol when I said 90! I didn't mean factorial 90 IIt was just an exclamation mark - I didnt see that at the time!!!

Answer 22

i was jk haha

Answer 23

thank you @welshfella and @ganeshie8 :)

Answer 24

oh ok! - I like using exclamation marks...

Answer 25

yw