a box contains 13 red balls and 26 bule balls. 2 balls are simultaneously taken random, prob r both same color

Answer 1

The above answer by blahb31 is correct. I think it is a little easier to count the possible outcomes first.
There are 39 balls. There are C(39,2)=741 possible two-ball combinations where C(a,b) = a! / [(a-b)!b!] .
Out of these, C(13,2)=78 are both red, while C(26,2)=325 are both blue.
Therefore, the probability is (78+325)/741 = 403/741 = 31/57
= 0.543859649....

Answer 2

P(Both are same color) = P(Both are red or both are blue) (With an "or" in a probability you use an addition rule)
= P(Both are red) + P(Both are blue) since these events are mutually exclusive.

Let's look at the probaliities on the right hand side individually.

P(Both are red) = P(1st is red and 2nd is red) (With an "and" in a probability you use a multiplication rule.)
= P(1st is red)P(2nd is red | 1st is red) since these events are not independent.
= (13/39)(12/38)
= 156/1482

P(Both are blue) = P(1st is blue and 2nd is blue)
= P(1st is blue)P(2nd is blue | 1st is blue)
= (26/39)(25/38)
= 650/1482

So going back to what we started with.

P(Both are the same color) = 156/1482 + 650/1482
= 806/1482
= 0.544

edit: Scott R, most elementary statistics students are not taught counting rules, so they might not necessarily know that method. This is why I take this approach when answering these questions.

Valmiki, there is no difference. Drawing two balls together is the same as drawing one ball, then drawing another without replacing the first.

Answer 3

I think the statistics professor is wrong here, as she is working with first and second balls.

Your question specifically states two balls are simultaneously taken, so there is no first or second ball.

It's more like what are the chances that a red ball is next to a red ball, or a blue ball is next to a blue ball when the two are taken out together.

Answer 4

(13/(13 + 26))(12/(12 + 26)) =
(13/39)(12/38) =
(1/3)/(6/19)
(6/57)
(2/19)

Probability of both being red is 2:19 or about 11% chance.

------------------------

(26/(13 + 26))(25/(13 + 25))
(26/39)(25/38)
(650/1482)
(325/741) or about 44% probability if both are blue.

Answer 5

prob there is two red =
1/3 * 12/38 = 0.3157

two blue
2/3 * 25/38 = 0.6578

So [0.3157+ 0.6578]/2=

48.67%