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?
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2 Answers
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Yes it's $0.5$. It's $\frac14 + \frac34 * \frac13$. You left out the $\frac34$ in your calculation.
Gregory Grant
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1Cheers, forgot to take into account that the 1/3 only happens 3/4 of the time! – Michael Crook Feb 16 '16 at 00:41
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@MichaelCrook No problem, it's an easy mistake to make. BTW please hit the check mark so it will be removed from the unanswered queue, thanks! – Gregory Grant Feb 16 '16 at 00:43
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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
$$\frac{1}{4}*1 + \frac{3}{4}*\frac{1}{3}= \frac{3+3}{12}= \frac{1}{2}.$$
Roland
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