Question

Help ASAP I really appreciate it. I such a probability and need to learn this.

A bag of marbles contains 12 red marbles, 8 blue marbles, and 5 green marbles. If three marbles are pulled out, find each of the following probabilities. In each we specify either replacement (the marbles go back into the bag after each pull) or no replacement.

A. Find the probability of pulling out 3 marbles of the same color without replacement. (More complex)

D. Find the probability of pulling out two blue marbles and one green marble in any order with replacement. Be careful as there are multiple ways this

Answer 1

so @Angel_Kitty12
will work through this with you:
Q1. how many marbles in the bag total at the start?
Q2. probability the first marble pulled out is a red?
Q3. probability the first marble pulled out is a blue?
Q4. probability the first marble pulled out is a green?

Answer 2

25 marbles in total. There are 12 red and the probability of them being replaced is 0.110592
There are 8 blue so that total will be 0.032768
And there are 5 green so
0.008

I think unsure here

Answer 3

First marble oh wait

Answer 4

If the first marble pulled out is red, would the fraction form be 12/25 still?

Answer 5

And with the blue and green marble its
8/25 and 5/25. Right? Then do I multiply them together or....

I'm very confused. So sorry

Answer 6

25 total = correct
A: same colour (without replacement)
RED = 12/25 x 11/24 x 10/23 = ?
GREEN = 5/25 x 4/24 x 3/23 = ?
BLUE = 8/25 x 7/24 x 6/23 = ?

Answer 7

Oh I read the question wrong! I thought it said with replacement! No wonder I wasn't understanding this

Answer 8

all good... so P(RED) = ?

Answer 9

So I multiply them together and add all three up to get approximately 0.16 or 0.155556174?

Red= approximately 0.096
Blue= 0.021504
Green= 0.0384

Right?

Answer 10

i got .0244 for blue?

Answer 11

@angel_kitty12
In probability it is preferable to work with fractions because they are exact, while decimals need to be rounded off, so inexact.

Answer 12

Or do I multiply all three after finding the sum

Answer 13

Okay so to work with fractions instead I got 336/13800

Answer 14

For blue

Answer 15

Which is 0.02434

Answer 16

I multiplied wrong your right

Answer 17

.0957 = red = 11/115
.0044 = blue = 1/230
.0244 = green = 14/575

Answer 18

cools :) all good then

Answer 19

Okay

0.096 or 1320/13800 for red
0.0244 or 336/13800 for blue and
0.0043 or 60/13800 for green

Answer 20

But I rounded wrong okay I got it now

Answer 21

also @Angel_Kitty12 be careful what you say around mathmale, the guy tends to abuse the ban powers he has as a moderator, so dont break the code of conduct if u see him online or in ur post

Answer 22

Now what's the next step? Do I add them all or multiply them all?

Answer 23

add them

Answer 24

Oh okay. That's odd

Answer 25

p(3 of 1 colour) = P (3red) + P(3 green) + P(3 blue)

Answer 26

Okay I got 0.1245

Answer 27

= 143 / 1150 = .1244... so yeah, perfect!

Answer 28

Okay cool! Now for part b though.. Will I do something similar to this?

Answer 29

i only see parts A and D posted...?

Answer 30

D I mean. That's supposed to be B

Answer 31

Autocorrect

Answer 32

ah, cool
so, what are the combinations that give us 2 blue and 1 green?

Answer 33

as i see it:
G B B
B G B
B B G
yeah?

Answer 34

Okay 2 blue and one green. I know the factions are 8/25 and for green its 5/25

If it's replaceable, will it be

P(8/25•8/25)+ P(5/25)?

Answer 35

Oh I thought something else never mind I see what your doing

Answer 36

no i think ur right, i didnt notice that this one was replaced each time

Answer 37

P(8/25) * P(8/25) * P(5/25)
+
P(8/25) * P(5/25) *P(8/25)
+
P(5/25) * P(8/25) * P(8/25)

... is that right?

Answer 38

Wait I'll have to add the equations three times?

Answer 39

well... yeah... i think so?
otherwise you're just working out the probability for the ones taken out in that order only i think?

Answer 40

Oh okay I get why

Answer 41

Well it seems right I mean it's reasonable

Answer 42

So when I work it out, I get 0.9072 correct?