Question

a bag contains 2 green marbles, 4 blue marbles, and 5 red marbles. What is the probability of choosing 2 blue marbles, if the first marble is returned to the bag before the second marble is chosen?

Answer 1

total number of marbles is 11 and the probability that the first one is blue is
\[\frac{4}{11}\]
also the probability that the second one is blue is
\[\frac{4}{11}\] and you want the probability that they are both blue. answer is
\[\frac{4}{11}\times \frac{4}{11}\]

Answer 2

make a tree diagram it's way easier to understand what's happening here.

Answer 3

if the first one was not returned to the bag it would be
\[\frac{4}{11}\times \frac{3}{10}\]

Answer 4

slow down

i dont understand anything

Answer 5

i will help you anikate

Answer 6

k thx

Answer 7

you can make a tree, but it is a fact that since the events are independent (meaning the outcome of one doesn't change the outcome of the other) that
\[P(A\cap B)=P(A)\times P(B)\]

Answer 8

memorizing formulas won't get you anywhere in life lol

Answer 9

i am just 7th grade

Answer 10

true but if you want to compute things you will need to know under what circumstances to add, subtract, multiply or divide

Answer 11

plz help me with my question

Answer 12

how many marbles in the bag total?

Answer 13

start out with 3 lines...one for green one for blue and one for red. mark on each line the probability for that specific color on the first pick. for example, red would be 5/11, blue 4/11, green 2/11.

Answer 14

since you are replacing the marble you took, the probability doesn't change on the second pick

Answer 15

2

Answer 16

hello?

Answer 17

plz help me

Answer 18

anikate i answered you, look up

Answer 19

nothing came up

Answer 20

hello?

Answer 21

start out with 3 lines...one for green one for blue and one for red. mark on each line the probability for that specific color on the first pick. for example, red would be 5/11, blue 4/11, green 2/11.
since you are replacing the marble you took, the probability doesn't change on the second pick. it's 4/11X4/11. So 16/121

Answer 22

still got nothing

Answer 23

Ok, look. You don't need to worry about the probabilities for the red and green marbles since it's only the blues you care about. Just compute the probability of choosing a blue marble first.

Answer 24

How many blue marbles are in the bag?

Answer 25

2

Answer 26

"a bag contains 2 green marbles, 4 blue marbles, and 5 red marbles."

There are 4 blue marbles right?

Answer 27

no 2 blue

Answer 28

Type the problem again?

Answer 29

a bag contains 2 green marbles, 4 blue marbles, and 5 red marbles. What is the probability of choosing 2 blue marbles if the first marble is returned to the bag before the second marble is chosen?

Answer 30

um hello?

Answer 31

ready?

Answer 32

yes

Answer 33

we do this in 3 easy steps

Answer 34

how many marbles in the bag total?

Answer 35

11 marbles

Answer 36

right. how many are blue?

Answer 37

4 blue marble

Answer 38

exactly. now what is the probability that if you pick one at random you get a blue one?

Answer 39

4/11

Answer 40

which is the same question as "what is the ratio of the number of blue marbles to the total number of marbles?"
yes you have it!

Answer 41

but

Answer 42

so the probability the first marble is 4/11

Answer 43

o

Answer 44

we are not done yet, but almost

Answer 45

wait

Answer 46

i wait

Answer 47

4/ll for blue

Answer 48

right

Answer 49

yes

Answer 50

k

Answer 51

site is slow be patient

Answer 52

ok now if you are going to pick two blue marbles, both the first and second have to be blue. that is clear yes?

Answer 53

yup

Answer 54

so you know your first marble was blue, otherwise you cannot pick 2 blue ones yes?

Answer 55

now you have picked a blue marble. you put it back in the bag. how many marbles are in the bag?

Answer 56

11

Answer 57

how many are blue?

Answer 58

4

Answer 59

yes

what is the probability you pick a blue marble on the second try?

Answer 60

4/11

Answer 61

exactly!

Answer 62

ok now we finish the question. in order for them BOTH to be blue we must pick a blue marble on the first try AND pick a blue marble on the second try yes?

Answer 63

Good stuff satellite.

Answer 64

yeah well now comes the tricky part!

Answer 65

for the probability that BOTH are blue we have to take the probability of each and multiply them together!

Answer 66

16/121

Answer 67

our last job is to take
\[\frac{4}{11}\times \frac{4}{11}\]

Answer 68

that is what i get, yes. you have it and we are done unless you want to do another one

Answer 69

i have other questions

Answer 70

ask one here and we can do it together

Answer 71

k

Answer 72

here it goes

Answer 73

there is a prisoner

Answer 74

and there are 3 routes for her to escape

Answer 75

route A has 1/4 chances of being successful

Answer 76

route b is 1/5

Answer 77

route c is 1/6

Answer 78

got it so far

Answer 79

and

Answer 80

the probability of selecting each route is 1/3

Answer 81

what is the probability that she might successfully escape by using road B

Answer 82

ok got it

Answer 83

we proceed just like the last one.

Answer 84

k

Answer 85

first if she is going to get out using road B two things must happen.
first she must choose road B yes?

Answer 86

yes

Answer 87

what is that probability?

Answer 88

probability of selecting each route is 1/3

Answer 89

2 minutes i will be right back

Answer 90

ok so it is 1/3
then if she select road B what is the probability that she escapes?

Answer 91

ok write when you get back

Answer 92

1/5

Answer 93

ok got it

Answer 94

now what is the probability that they BOTH occur?

Answer 95

huh?

Answer 96

first the prisoner has to pick the road. then he has to escape. BOTH have to happen yes?

Answer 97

same as previous problem where BOTH marbles have to be blue

Answer 98

yes