A bag has five red marbles, six blue marbles, and four black marbles. What is the probability of picking a blue marble, replacing it, and then picking a red marble? I can't get this right, I have four anwser to choose from and no matter what I do I can't find the right option.

Question

trevor12 · Answer

ill try

thesmartone · Answer

How many marbles are there total?

shaofluff · Answer

15 marbles in total.

shaofluff · Answer

I can do this easy if it were just deciding the probability of picking one blue marble, but the replacing it and picking the color red marble after the blue is what stumps me.

bigdreams · Answer

Does it give you answers to choose from or do you have to find the answer?

shaofluff · Answer

I have the options 8/75, 3/5, 2/15, and 4/45 to choose from.

bigdreams · Answer

hm...

shaofluff · Answer

I don't need an anwser right away, I just want some help

thesmartone · Answer

How many marbles are blue?
How many marbles are red?

shaofluff · Answer

Six blue marbles, five red marbles, but there is also the extra 4 black marbles to think about.

thesmartone · Answer

ignore the 4 black marbles :P

what is the probability of picking a blue marble?

It's how many blue marbles there are over how many total marbles there aer

thesmartone · Answer

are*

shaofluff · Answer

6/15 would be the probability of picking a blue marble out of the 15 marbles we have :P

shaofluff · Answer

Also it is 5/15 or 1/3 to get a red marble out of the 15 marble

thesmartone · Answer

and let's say he got lucky and got a blue marble. Not he puts back the blue marble in to the bag.

Now, what is the probability of choosing a red marble?

thesmartone · Answer

that's correct :)

thesmartone · Answer

can you reduce 6/15 also?

hint: both numbers are divisible by 3

shaofluff · Answer

Well yes, I just forgot to reduce it, you can get it to 2/5.

thesmartone · Answer

ok, now we multiply the probabilities

2/5 * 1/3 = ?

remember, when multipling fractions, you multiply the numerators and multiply the denominators. You do not need the same denominator to multiply fractions

shaofluff · Answer

2/15 would be the anwser for multiplying 2/5 and 1/3

shaofluff · Answer

So would that be my anwser? 2/15? I just didn't know how to deal with using those two fractions to get the probability after putting the blue marble back then picking a red marble.

thesmartone · Answer

2/15 is the answer :)

shaofluff · Answer

Thank you so much! Now if this comes up again in another test I will know how to do it, you're great, you got my best response medal :P

thesmartone · Answer

Anytime! :)

thesmartone · Answer

Let me try to explain why we multiply it

The probability of choosing a red marble after choosing a blue marble

There's a 2/5 chance of getting a blue marble.

Now let's say, you got lucky and you get the blue marble.

You replace it and are going for the red one. And you get the red marble, which was a 1/3 probability.

The probability of getting a red marble after getting a blue marble and replacing it is going to be 2/5 * 1/3

thesmartone · Answer

Now, if they tell you they did NOT replace the blue marble you would have to do this:

6/15 * 5/14 = 

2/5 * 5/14 = 

2/1 * 1/14 = 

2/14 = 

1/7

shaofluff · Answer

Okay yeah, that does make sense now, thanks for teaching me instead of just giving me an anwser. I wrote a testimonial for you and became a fan :D Thanks for the help

thesmartone · Answer

Anytime! Also, if anyone gives you an answer, it's against the rules of this site. (You can view the rules here: http://openstudy.com/code-of-conduct ) Also, welcome to OpenStudy!