Suppose , there are 3 red balls and 2 black balls in a box .
I have to find probability of choosing 2 black balls .
Then what is wrong with this solution .
for 1st ball being black 2/5 , and for second ball being black it is 1/4 , after 1st ball is black .
Then total probability is 1/10 .
If I do , 2C2/5C2 answer is 1/10 .
what is the difference in these two approaches ? Will they always yield the correct answer ?
What if the events aren't independent ?
For the first choice there are two black balls in the box out of five balls in total so the probability of choosing a black ball is 2/5 not 1/5
For the edited version: One method you can think of as looking at the problem step by step whereas one looks at the entire process as a whole i.e. do I look at the choices for each individual ball picked or just the overall choices for two balls. Both are valid for these problems and give the same answer. In the case of independent events, the second method won't work as $^nC_r$ chooses r objects from n but inherently without repetition whereas independent events allow for repetition.