- #1

- 199

- 21

- TL;DR Summary
- In a bowl you got 3 white and 4 black marbles.

Pick 2 at random without putting back the marble you picked.

What's the probability of you picking one white and one black marble?

My approach is the amount of successfull options / total amount of options.

I can first pick white in 3 different ways. Then black in 4 different ways

3 * 4

But I can also pick black first then white

4 * 3

Total amount of ways to pick marbles are

7 *6

So the probability is:

(3*4 + 4 * 3) / (7 * 6) = 4/7

which is correct.

But my question is, how do I know how many ways I could've picked successfull options?

In this case it¨'s obvious that I can pick 3 * 4 and 4 * 3 only, but if I have more colored marbles to pick from etc. What's the formula for that?

I don't see how it could be combinations, 7 Choose 2? or 4 Choose 1? Maybe it's binominal 2 over 1 but what does that even mean?

I can first pick white in 3 different ways. Then black in 4 different ways

3 * 4

But I can also pick black first then white

4 * 3

Total amount of ways to pick marbles are

7 *6

So the probability is:

(3*4 + 4 * 3) / (7 * 6) = 4/7

which is correct.

But my question is, how do I know how many ways I could've picked successfull options?

In this case it¨'s obvious that I can pick 3 * 4 and 4 * 3 only, but if I have more colored marbles to pick from etc. What's the formula for that?

I don't see how it could be combinations, 7 Choose 2? or 4 Choose 1? Maybe it's binominal 2 over 1 but what does that even mean?