# Probability of Drawing A Card at least once (with replacement)

Say we have a standard deck of $52$ cards. Probability of drawing the King of Hearts is $\frac{1}{52}$ obviously.

But lets say we were to make $30$ draws with replacement (so each time the card is drawn, it is put back in the deck and and the deck is shuffled). What are the odds that the King of Hearts card was drawn at least once out of those $30$ draws?

Thanks

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• Thank you @JKnecht and @probablyme! – Nullqwerty Feb 4 '16 at 1:53

Let $K$ be the number of KOHs you draw. Since each draw is with replacement and (presumably) independent of another, then it is easier to start and calculate the complement, $$P(K\geq 1) = 1-P(K=0),$$ in 30 draws.
• @Nullqwerty Almost, $1-\left(\frac{51}{52}\right)^{30} = 0.4415234 \approx 44\%$. – Em. Feb 4 '16 at 1:51