An urn contains 5 Red, 4 White, and 6 Blue marbles. Two marbles are drawn at random, without replacement. Determine the probability that:

Question

a. A Red marble is drawn, and then a White marble.

b. A White marble is drawn, and then a Red marble.

c. A Red and White marble are drawn (in either order).

d. The second marble drawn is white, given that the first marble drawn is white.

e. The first marble drawn is white, given that the second marble drawn is white.

Answer 1

Hi Again Chris;

Let's begin with

5R+4W+6B=15M

a. A Red marble is drawn, and then a White marble.

((5/15)(4/(15-1))=probability

The (15-1) is because there is no replacement.

(5/15)(4/14)=probability

(0.33)(0.29)=0.0957=9.57%

b. A White marble is drawn, and then a Red marble.

(4/15)(5/(15-1))=probability

(4/15)(5/14)=probability

(0.27)(0.36)=0.0972=9.72%

c. A Red and White marble are drawn (in either order).

[(5/15)(4/(15-1))] + [((4/15)(5/(15-1))]=probability

[(0.33)(0.29)]+[(0.27)(0.36)]=probability

[0.0957]+[0.0972]=0.1829=18.29%

d. The second marble drawn is white, given that the first marble drawn is white.

[((4-1)/(15-1))(4/15)]=probability

[(3/14)(4/15)]=probability

[(0.21)(0.27)]=probability

0.0567=5.67%

e. The first marble drawn is white, given that the second marble drawn is white.

same as d, except the sequence is different.

I love math.  So please keep those questions coming...

Answer 2

Hi Vivian,

Iwill suggest this way:

 

case a. (5/15)(4/14)=(5x4)(15x14)=20/210=2/21

 

case b. (4/15)(5/14)=(4x5)(15x14)=20/210=2/21

 

Using fraction instead decimal numbers avoid mistakes!

Answer 3

Hey Chris,

So the way to figure this out is to determine the probability of picking the red marble (number of red marbles=5/total marbles=15), which is 5/15. Then, determine the probability of picking a white marble (number of white = 4/total number, which is now 14), so the probability would be 4/14. Multiply the two together to get 20/210=9.5%

 

The same application is applied to the rest of the problem. Always take the number of marbles of that color divided by the total. If the marbles are not replaced then you subtract one from the total.

 

To visually see the application use the following formula:

 

  # of color                   # of color            

  -----------           X     ------------               etc.......     

total # marbles           total # marbles         

 

 

This same application is applied depending on number of marbles drawn. Let me know if this helps.