Question

a bag contains 3 red marbles, 4 green marbles.. A marble is drawn from a bag and not put back before 2nd marble is drawn. What is the probability that 2nd marble drawn is red?

Answer 1

So either the first marble can be red AND the second marble can be red, or the first marble can be geen and the second marble can be red. What do you think you have to do?

Answer 2

P(E) = (3/7 * 2/6) + (4/7 * 3/6) = ....

Answer 3

Also, if you were wondering, there are 7 marbles in the bag, but when you take one out, you do not put it back, so thre's only 6 left.

Answer 4

the probability is first marble red,second red or first green then second red i.e. P(RR) OR P(GR) \[\frac{ 3 }{ 7 }\times \frac{ 2 }{ 6 }+\frac{ 4 }{ 7 }\times \frac{ 3 }{ 6 }=\frac{ 1 }{ 7 }+\frac{ 2 }{ 7}=\frac{ 3 }{ 7 }\]

Answer 5

ready to get help?

Answer 6

So, we are starting with 3 red, 4 green, 7 total marbles. And we draw one out. Lets start with the first one.

Answer 7

It could be red, or green, right?

Answer 8

@nylejre are you there?

Answer 9

Do you know how to find the probability that it could be green?

Answer 10

if not. When looking at just drawing one of the marbles out, we can find the probability of a certain color by dividing the number of marbles of that color by the total marbles in the bag.

Answer 11

I'll have to leave sine your not ready to get help.

Answer 12

I have 3/7 because there are 3 possible red marbles to draw, and 7 total marbles.

Answer 13

so do the same with the green 4/7

Answer 14

Now, we know that the first marble chosen is not replaced, so the number of marbles in the bag is now 6, correct?

Answer 15

we can draw this if you like, just depends.

Answer 16

next we want to find the probability that the second marble drawn is also red.

Answer 17

So. We have 2 different options. We could have the 1st marble be red, and the 2nd marble be red. Or, we could have the 1st marble be green, and the 2nd marble be red.

Answer 18

Lets look at option 1, both marbles are red.

Answer 19

so what's the probability that the 2nd marble will be red?

Answer 20

Note* It could be either one, you have to consider both options, unless you are told otherwise.

Answer 21

Ok. So now we have 6 total marbles, and only 2 red

Answer 22

ok wait.. i'll just analyzed the first thing you did..

Answer 23

Since we have 2 red left, and 6 marbles, the probability will be 2/6. Now that we know that, we need to find the probabilty that both draws are red.

Answer 24

alright then. I'll continue with me explanation in the meanwhile.

Answer 25

Since we have 2 red left, and 6 marbles, the probability will be 2/6. Now that we know that, we need to find the probabilty that both draws are red.
To do that, we multiply our probability that the first draw is red (3/7) by the probability that the 2nd draw is also red (2/6)

Answer 26

Does that make sense?

Answer 27

Now we can work on the second option, 1 green, 1 red.

Answer 28

To multiply fractions, you can use your calculator to get a decimal, or you can multiply the numerators by the denominators... For example, (3*2)/(7*6)
That will give you a fraction for your answer. Either should be fine

Answer 29

1/7

Answer 30

Yup good!

Answer 31

are you clear up to that?

Answer 32

Okay that was a part, now we have to find the probability of the second option, which
is one green, 1 red.

Answer 33

Now, we find the probability that the 2nd marble is red.

Answer 34

If the first green marble isn't replaced, we have only 6 marbles, and 3 of them are red, correct?
so...

Answer 35

... Now, we have mulitply these probabilities to find the probability that the first marble drawn is green AND the second marble drawn is red.

Answer 36

4/7 * 3/6?

Answer 37

2/7

Answer 38

= 2/7 correct? :)

Answer 39

yeah

Answer 40

any questions on that?

Answer 41

Ok. For the second marble to be red, we could have either one of these 2 options occur, so the total probability that the 2nd marble is red is the sum of these 2 probabilities.

Answer 42

or 1/7 + 2/7

Answer 43

what is 1/7+ 2/7?

Answer 44

the answer is 3/7 Yes. That should be your final answer.

Answer 45

I hope I help answer your question, and hopefully by now your confusion is recovered. Have a great day, and feel free to ask any other questions.

Answer 46

Bye for now!

Answer 47

waahh... you did great!! I understand it better now.. thanks a lot!

Answer 48

anything else before I leave, are you all confirmed?

Answer 49

That is great to hear, I hope your feeling much better with these kind of problems.