Question

PLEASE HELP I NEED YOUR HELP GUYS PLEASE !

Answer 1

Total = 16 marbles
R = 4
B = 7
G = 5

a)
P(R) = 4/17
with replacing it P(B) =  7/17
so 
P(R, then B) = 4/17 x 7/17 = 28/289

b)
P(R) = 4/17
no replacing, P(B) = 7/16
so 
P(R, then B) = 4/17 x 6/17 = 24/289

c)
The answers to parts a and b are not the same. 
Part a (28/289)  with replacing, the probability to select a red then blue is higher then part b (24/289)

Answer 2

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.

$\frac{4}{16} * \frac{7}{16} = \frac{28}{256} = \frac{7}{64}$

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.

$\frac{4}{16} * \frac{7}{15} = \frac{28}{240} = \frac{7}{60}$

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.