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.
[tex] \frac{4}{16} \ or\ \frac{1}{4} [/tex]

Next, the probability of selecting a blue marble.
[tex] \frac{7}{16} [/tex]

Multiply the probabilities together.
[tex] \frac{1}{4} * \frac{7}{16} = \frac{7}{64} [/tex]
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.
[tex] \frac{4}{16} \ or\ \frac{1}{4} [/tex]

Next, the probability of selecting a blue marble WITH A RED MARBLE REMOVED.
[tex] \frac{7}{15} [/tex]

Multiply the probabilities together.
[tex] \frac{1}{4} * \frac{7}{15} = \frac{7}{60} [/tex]
That is the probability for event b.

c.
Obviously:
[tex] \frac{7}{64} \neq \frac{7}{60} [/tex]
So the answer is no.