you need to draw 1 card with 4 cards left and 2 draws

Question

I was wondering what are the odds of drawing the 1 card you need when you have 4 cards left and two draws.

I instinctively think 50/50 as you have two draws, but then I think it's a 1/4 + 1/3 == > 50/50

What is correct and why?

Answer 1

Yes it's $0.5$. It's $\frac14 + \frac34 * \frac13$. You left out the $\frac34$ in your calculation.

Answer 2

The probability to draw the card you want with the first draw is $\frac{1}{4}$. What you draw in the with the second draw doesn't matter.

If you don't draw your card with the first draw (this has probability of $1-\frac{1}{4}=\frac{3}{4}$), then you have one out of three cards left, i.e. probability of drawing in this case is $\frac{1}{3}$, thus your total probability is

$$\frac{1}{4}*1 + \frac{3}{4}*\frac{1}{3}= \frac{3+3}{12}= \frac{1}{2}.$$