1. ## [SOLVED] Depend event

hai every body... i still stuck until now for the following problem. hope somebody can guide me.

Question
A box contains 5 black cubes and 3 red cubes. Two cube are drawn at random from the box. find the probability that :
(a) both cubes are black
(b) both cubes are the same colour
(c) both cubes are different colours

ans given:
5/14, 13/18 ( i also confuse this ans for which question (a)/ (b) or (c)

My solution:
(a) P( both cubes are black ) = P (Black,Black)
= 5/8 * 5/8
= 25/64

(b) P (both cubes are the same colour) = P (Black,Black) + P (Red,Red)
= 25/64 + 3/8*3/8
= 25/64 + 9/64
= 34/64
= 17/32
Remarks: base on my calculation it look like it wrong when i compare it with the given ans..

2. remember that the second time you take a ball out there are less balls in the box i.e the first time you take a ball out the chance of it being black is 5/8 but now there are 4 black balls left and 7 balls left in total.

sorry, cubes

3. Originally Posted by Tarzan
remember that the second time you take a ball out there are less balls in the box i.e the first time you take a ball out the chance of it being black is 5/8 but now there are 4 black balls left and 7 balls left in total.

sorry, cubes
but this question not stated with replacement or without replacement
. is it we can consider without replacement for this case

4. Originally Posted by nikk
but this question not stated with replacement or without replacement
. is it we can consider without replacement for this case

i find if it's not stated either way the cubes generally aren't replaced, but it does depend on who wrote the question.

5. Originally Posted by Tarzan
i find if it's not stated either way the cubes generally aren't replaced, but it does depend on who wrote the question.
i try to calculate it now base on your info

6. ## ans to confirm

base on your info this is my ans:

(a) P( both cubes are black ) = P (Black,Black)
= 5/8 * 4/7
= 5/14 (same as per ans)

(b) P (both cubes are the same colour) = P (Black,Black) + P (Red,Red)
= 5/8 * 4/7 + 3/8*2/7
= 13/28 ( not same with ans given)

(c) both cubes are different colours
= P ( Black,Red) + P( Red,Black)
= 5/8 * 3/7 + 3/8*5/7
= 15/28 ( not same with ans given)

any one can confirm my ans

7. There is a typo in the second given answer. It should be $\displaystyle \frac{13}{{\color{red}2}8}$.
Both the same color is: $\displaystyle \frac{(5)(4)+(3)(2)}{(8)(7)}$

8. Originally Posted by Plato
There is a typo in the second given answer. It should be $\displaystyle \frac{13}{{\color{red}2}8}$.
Both the same color is: $\displaystyle \frac{(5)(4)+(3)(2)}{(8)(7)}$
thank you both of you.....
any command to my ans???

If they are not the same color then they are different colors. Right?

10. Originally Posted by Plato
If they are not the same color then they are different colors. Right?
it mean u agreed to my ans??

11. Originally Posted by nikk
it mean u agreed to my ans??
Well, yes.