Question

Probability help.

What is the probability of drawing {a jack of spades, a 7 of clubs, a queen of hearts} from a standard deck of cards WITH replacement?

A. 1/52 x 1/51 x 1/50
B. 1/8
C. (1/52)^3
D. 0.064

Answer 1

replacement means you put back the card after you've drawn it right?
so the probs don't change for 2nd, 3rd draw

Answer 2

Right. So it can't be A, right?

Answer 3

because I did not think about the probability of the cards
I have no clue :D

Answer 4

well jack spade is just once in there right ?

Answer 5

every card is just once in there

Answer 6

LMAO ohh lord. To be honest I have noooooo idea what a standard deck of cards is -.-

Answer 7

So there's like one of each but different colours?

Answer 8

Like black and red

Answer 9

right

I think every type of card is in all " 4colors"
since they specify both
then what they specify exists only once

Answer 10

Well the color in the question is black I assume they mean only a black colour of each

Answer 11

what's the # of cards in a deck? if we have this we can calculate how likely it is to draw exactly one card from it

Answer 12

There are 52 cards in a standard deck according to Siri lol

Answer 13

:D ok

Answer 14

so since all of the cards they listed, I'm pretty sure only occur once in the deck
then the chance to draw each of the cards is 1/52

Answer 15

so when we draw the first card, we already have a 51/52 chance that we violated the correct sequence.

Answer 16

and then there are 3 different card choices or whatever... does C make sense?

Answer 17

and then when we actually managed to draw the correct card (just 1/52 chance!!) then we draw again and SURELY this time the 51/52 will stop us
from completing the correct sequence

Answer 18

we would need to get the 1/52 chance INSIDE OF THE INITIAL 1/52 chance, to make it to the last card

Answer 19

only the best reach level 2, and then 51/52 of those that managed still die...

Answer 20

\[\frac{ 1 }{ 52 } \times \frac{ 1 }{ 52 } \times \frac{ 1 }{ 52 }\]

Answer 21

So ot's like practically impossible unless you a cheater/magician -.- lol I got like 0.0068 and a bunch of other numbers 0.o

Answer 22

it's*

Answer 23

yeah :)

if you follow along a track of chances, you multiply them
so that's why we multiplied each chance with each other,
because we're only interested in the complete, correct trail.

the trail is much less likely than getting one of the three.

Answer 24

each probability has a 1/52 chance, but
getting all the three 1/52 in the right order......

is equal to multiplying all three chances

Answer 25

you can "simplify" this multiplication / write it without typing the same term thrice

Answer 26

So to me it looks to be either C or D 0.o

Answer 27

yep :)

Answer 28

multiplying fractions works like this
\[\frac{ 1 }{ 2 } \times \frac{ 1 }{ 2 }= \frac{ 1 }{ 4 }\]

Answer 29

(our probabilities ARE fractions, and they're multiplied so that's why it matters...)

Answer 30

all following three are the same thing:\[\frac{ 1 }{ 2 } \times \frac{ 1 }{ 2 }=(\frac{ 1 }{ 2 })^2=\frac{ 1 }{ 2^2 }\]

Answer 31

So it has to be in the form of a fraction?

Answer 32

our probabilities are fractions

Answer 33

well, you can transform fractions to the p= notation
1/4 = 25% = 0.25

in this case sticking to fractions makes most sense.

Answer 34

ok what have we learned
1)
2)
3)

Answer 35

So we're left with C! >:D

Answer 36

1) there are 52 cards in a deck, and the card they want is one of a type

chance to draw it is 1/52

Answer 37

^right

Answer 38

2) if you want a chain of probabilities you multiply them. we have a chain of three, so we multiply 1/52 three times in a row

Answer 39

3) we can re-write 1/52*1/52*1/52 like 1/52^3 :)

Answer 40

^check

Answer 41

So it is C!!! >:D muahaha

Answer 42

yep:)
and in case you wondered if D was also possible- the decimal chance to get the cards in the right order is:
1 / 140608
or
7,11e-6 = 0.000007 or something

Answer 43

only for magicians and cheaters.

Answer 44

Ahhh ok. All is straight in my head for now. Thanks man much appreciation

Answer 45

Lmfaooo!

Answer 46

:)