Suppose you choose a marble from a bag containing 4 red marbles, 2 white marbles, and 3 blue marbles. You return the first marble to the bag and then choose again. Find P(red and blue).
A. 4/3

B. 2/3

C. 7/9

D. 4/27

Question

Suppose you choose a marble from a bag containing 4 red marbles, 2 white marbles, and 3 blue marbles. You return the first marble to the bag and then choose again. Find P(red and blue). 
 A. 4/3  
 
 B. 2/3  
 
 C. 7/9  
 
 D. 4/27

anonymous · Answer

what do you think when you see the word "and"?

anonymous · Answer

multiply the probability that the first one is red times the probability that the second one is blue given that the first one is red, but since you are replacing the marble it doesn't matter if the first one is red or not, the probabilities will be the same

anonymous · Answer

4/3?

anonymous · Answer

you have 9 marbles all together, and of those 4 are red, so what is the probability that the first marble chosen is red?

anonymous · Answer

it is not $\frac{4}{3}$ for many reasons but the simplest one is that a probability is a number between 0 and 1 and $\frac{4}{3}$ is not, so make sure if you take a test or quiz not to answer with a number bigger than one

anonymous · Answer

out of 9 marbles, 4  are red
probability that the marble chosen at random is red is the ratio of the red marbles to the total, namely $\frac{4}{9}$
now you need to find the probability that the second one is blue 
can you do that?

anonymous · Answer

3/9

anonymous · Answer

good
now your last job is to multiply them together, assuming the question is asking "what is the probability the first is red and the second is blue

anonymous · Answer

is it clear what you need to do?

anonymous · Answer

12/81?

anonymous · Answer

yes, but reduce first, multiply last to make life easier

anonymous · Answer

you will get one of your choices if you do that i.e. if you reduce to lowest terms