Mathematics, 02.07.2019 02:30, tylorwsimmons
Luca keeps picking playing cards out of a standard deck of 52 cards, hoping he will draw an ace. there are four aces in the deck. after looking at each card, he places it back in the deck. what is the probability that luca will draw an ace in the first nine attempts?
Answers: 1
![=S+FS+FFS+FFFS+FFFFS+FFFFFS+FFFFFFS+FFFFFFFS+FFFFFFFFS\\\\=\frac{1}{13}+\frac{12}{13}*\frac{1}{13}+\frac{12}{13}*\frac{12}{13}*\frac{1}{13}+\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{1}{13}+\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{1}{13}+\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{1}{13}+\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{1}{13}+\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{1}{13}+\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{12}{13}*\frac{1}{13}\\\\=\frac{1}{13}*[1+\frac{12}{13}+(\frac{12}{13})^2+(\frac{12}{13})^3+(\frac{12}{13})^4+(\frac{12}{13})^5+(\frac{12}{13})^6+(\frac{12}{13})^7+(\frac{12}{13})^8]\\\\=\frac{1}{13}*[\frac{1-(\frac{12}{13})^9}{1-\frac{12}{13}}]\\\\=\frac{1}{13}*[\frac{1-(\frac{12}{13})^9}{\frac{1}{13}}]\\\\=1-(\frac{12}{13})^9\\\\=1-0.4866\\\\=0.5134{\text{approx}}](/tpl/images/0040/9248/73638.png)
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Luca keeps picking playing cards out of a standard deck of 52 cards, hoping he will draw an ace. the...
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