Answer to Question #100416 in Statistics and Probability for Taylor Meligan

Question

If you draw one card at a time (with replacement), what is the probability that the first face card you draw will be the tenth card?

Answer 1

If we draw one card at a time (with replacement), the probability that the card is the face card is

$$p=\frac{12}{52}=\frac{3}{13}$$

'The first face card you draw will be the tenth card' means that we draw 9 non-face cards and the tenth card was the face card. The probability that the first face card we draw will be the tenth card is given by

$$(1-p)^9p=\left(1-\frac{3}{13}\right)^9\frac{3}{13}=\frac{3000000000}{13^{10}}\approx 0.0218$$