The diagram below shows the contents of a jar from which you select marbles at random.
a. what is the probability of selecting a red marble, replacing it, and then selecting a blue marble? show your work.
b. what is the probability of selecting a red marble, setting it aside, and then selecting a blue marble? show your work.
c. are the answers to parts (a) and (b) the same? why or why not?

So,

There are 4 red marbles.
There are 7 blue marbles.
There are 5 green marbles.
There are 16 marbles in total.

a.
Answer = (probability of selecting a red marble)(probability of selecting a blue marble)
First, the probability of selecting a red marble.


Next, the probability of selecting a blue marble.


Multiply the probabilities together.

That is the probability for event a.

b.
Answer = (probability of selecting a red marble)(probability of selecting a blue marble)
First, the probability of selecting a red marble.


Next, the probability of selecting a blue marble WITH A RED MARBLE REMOVED.


Multiply the probabilities together.

That is the probability for event b.

c.
Obviously:

So the answer is no.