First, establish the amount of marbles in the jar, and the amount of marbles that belong to each color.
16 total marbles
4 red marbles
7 blue marbles
5 green marbles
a. The probability of selecting a red marble is as follows:
(red marbles / total amount of marbles)
The same will go for blue and green.
When you are finding out the probability of performing a sequence of events, you multiply the individual probabilities of each event occurring.
Find the probability of pulling a red marble.
4 red marbles / 16 total marbles = 4/16 chance of pulling a red marble
You are replacing the marble afterwards, so the total amount of marbles do not change.
Find the probability of pulling a blue marble.
7 blue marbles / 16 total marbles = 7/16 chance of pulling a blue marble
Multiply these probabilities together.
[tex] \frac{4}{16} * \frac{7}{16} = \frac{28}{256} = \frac{7}{64} [/tex]
There is a 7/64 chance of pulling a red marble, replacing it, then pulling a blue marble afterwards.
b.
Find the probability of pulling a red marble.
4 red marbles / 16 total marbles = 4/16 chance of pulling a red marble
You are setting the marble outside the jar, so subtract 1 from the total amount of marbles. You now have 15 marbles in the jar.
Find the probability of pulling a blue marble.
7 blue marbles / 15 total marbles = 7/15 chance of pulling a blue marble
Multiply these two probabilities together.
[tex] \frac{4}{16} * \frac{7}{15} = \frac{28}{240} = \frac{7}{60} [/tex]
There is a 7/60 chance of pulling a red marble, setting it aside, then pulling a blue marble.
c.
The answers are different because the total amount of marbles changed in b, while the total amount did not change in a.
