Question

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?

Answer 1

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.

`(4)/(16) \ or\ (1)/(4)`

Next, the probability of selecting a blue marble.

`(7)/(16)`

Multiply the probabilities together.

`(1)/(4) * (7)/(16) = (7)/(64)`
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.

`(4)/(16) \ or\ (1)/(4)`

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

`(7)/(15)`

Multiply the probabilities together.

`(1)/(4) * (7)/(15) = (7)/(60)`
That is the probability for event b.

c.
Obviously:

`(7)/(64) \\eq (7)/(60)`
So the answer is no.