Conditional Probability Of Picking Balls From A Box

A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the following events:

These are the values I have come up with that I think are right, I also think I have managed to answer 2 of the questions but am really struggling with the rest.

A: One of the balls is yellow (1/3)
B: At least one ball is red (3/5)
C: Both balls are green (1/5)
D: Both balls are of the same color (4/15)

a) P(not A|B) = ?
b) P(B|not D) = ?
c) P(Ac|B) = ?
d) P(Bc|D) = ?
e) P(C|D) = 3/4
f) P(D|C)= 1

Thanks so much!

rebecca94s said:

A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the following events:
These are the values I have come up with that I think are right, I also think I have managed to answer 2 of the questions but am really struggling with the rest.
A: One of the balls is yellow (1/3)
B: At least one ball is red (3/5)
C: Both balls are green (1/5)
D: Both balls are of the same color (4/15)

a) P(not A|B) = ?
b) P(B|not D) = ?
c) P(Ac|B) = ?
d) P(Bc|D) = ?
e) P(C|D) = 3/4
f) P(D|C)= 1

Click to expand...

We really do want to help you.
Did you read the rule's of this forum?
If not, then do so now.

Then you will understand that you must first post some effort or comment on each of these.

pka said:

We really do want to help you.
Did you read the rule's of this forum?
If not, then do so now.

Then you will understand that you must first post some effort or comment on each of these.

Click to expand...

Sorry I forgot to show that I had actually put effort in already,

The original question was this:
A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the following events:
A:

One of the balls is yellow

B:

At least one ball is red

C:

Both balls are green

D:

Both balls are of the same color

I was able to come up with these values on my own:
A: One of the balls is yellow (1/3)
B: At least one ball is red (3/5)
C: Both balls are green (1/5)
D: Both balls are of the same color (4/15)

I was also able to come up with the answer to 2 of the questions but am unsure of how to proceed with the rest.
a) P(not A|B) = ?
b) P(B|not D) = ?
c) P(Ac|B) = ?
d) P(Bc|D) = ?
e) P(C|D) = 3/4
f) P(D|C)= 1
thanks again and sorry for the misunderstanding

rebecca94s said:

A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the following events:

These are the values I have come up with that I think are right, I also think I have managed to answer 2 of the questions but am really struggling with the rest.

A: One of the balls is yellow (1/3)
B: At least one ball is red (3/5)
C: Both balls are green (1/5)
D: Both balls are of the same color (4/15)

a) P(not A|B) = ?
b) P(B|not D) = ?
c) P(Ac|B) = ?
d) P(Bc|D) = ?
e) P(C|D) = 3/4
f) P(D|C)= 1

Thanks so much!

Click to expand...

Your probabilities for events A,B,C,D are correct.
Also, your conditional probabilities e and f are correct.

There are two ways to approach the conditionals - either by thinking through by counting possibilities the same way you found A,B,C,D, or else by using theorems. For instance, for (a),

P(A | B) = P(A∩B) / P(B),...and...P(notA | B) = 1 - P(A | B)

The intersection A∩B requires one yellow and one red.

What do Ac and Bc mean in (c) and (d)?

Give us some more of your work on (a)-(d), and we will try to guide you further.