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14.Probability
normal
All the spades are taken out from a pack of cards.From these cards, cards are drawn one by one without replacement till the ace of spade comes. The probability that the ace of spade comes in the $4^{th}$ draw is
A
$\frac{4}{13}$
B
$\frac{12}{13}$
C
$\frac{1}{13}$
D
$\frac{10}{13}$
Solution
The probability of not drawing ace in first, second, third draw respectively are $\frac{12}{13}, \frac{11}{12}, \frac{10}{11}$ respectively.
Probability of drawing ace of spade in $4^{\text {th }}$ draw $=\frac{1}{10}$ required prob. $=\frac{12}{13} \times \frac{11}{12} \times \frac{10}{11} \times \frac{1}{10}=\frac{1}{13}$
Standard 11
Mathematics
