# Math Help - [SOLVED] Depend event

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 $\frac{13}{{\color{red}2}8}$.
Both the same color is: $\frac{(5)(4)+(3)(2)}{(8)(7)}$

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