Question

A bag contains 3 red marbles, 2 blue marbles and 5 green marbles. What is the probability of selecting a blue marble, replacing it in the bag and then selecting a green marble?
A. 7/10
B. 4/5
C. 3/20
D. 1/10
I keep getting 1/12 can someone explain where I am going wrong.

Answer 1

what is the probability of first selecting a blue marble?

Answer 2

2/8

Answer 3

why do you say that?

Answer 4

I excluded the blue marbles out of the overall total, which is 8 marbles left and two blue marbles that can be chosen

Answer 5

there are 2 blue marbles in a bag of 10 marbles. if you reach in and grab one, the probability it is blue is just the number of blue marbles divided by the total number of marbles

Answer 6

2/10 + 5/10

Answer 7

yes. now, you replace the marble back in the bag and draw another one at random. what is the probability that you get a green one?

Answer 8

not so fast

Answer 9

5/10 is the probability of drawing a green one, yes. but you cannot simply add the probabilities as you have done.

Answer 10

if you had another step, adding the probabilities could give you a probability > 1 which iis impossible. therefore, that must not be how it works, right?

Answer 11

a certainty is a probability of exactly 1.

Answer 12

so if 2/10 and 5/10 is correct than I'm not understanding the extra step? Multiply? Divide? Add? Or Subtract?

Answer 13

these are what are called independent events. the second event does not depend on what happened in the first event. flip a coin once, then flip it again, and you have two independent events. the first coin flip does not affect the way the coin falls the second time you flip it.

Answer 14

So the replacing, doesnt matter

Answer 15

in the case of

Answer 16

drawing a green marble

Answer 17

to combine the probabilities of independent events, you multiply them.

so the probability of flipping a coin once and getting heads is 1/2. flipping again, the probability of getting heads remains 1/2. however, the probability of flipping twice and getting two heads is 1/2*1/2=1/4

you can also see this with an outcome table

H H
H T
T H
T T

4 different possibilities, but only 1 is two heads, so probability is 1/4

Answer 18

the replacing DOES matter. if you didn't replace the first marble, you would then be drawing from a bag with a different number and composition of marbles!

Answer 19

Okay

Answer 20

it would no longer be a bag with 3 red 2 blue 5 green, but a bag with 3 red 1 blue 5 green and probability of drawing green from that bag is 5/9

Answer 21

so its 1/10?

Answer 22

you betcha

Answer 23

if you didn't replace, what would the answer be?

Answer 24

that would be 2/10 and 5/9 .... 10/90 ?

Answer 25

which reduces to 1/9, yes. good.