Answer to Question #189307 in Statistics and Probability for Catalino satuito

Question

You choose a card at random from a standard deck of cards, replacing each card drawn, until you get a diamond. What is the probability that you will get a diamond in not more than 3 trials?

Answer 1

Solution:

P(getting a diamond card in not more than 3 trials) = P(getting a diamond card in 1 trial)+P(getting a diamond card in 2 trials)+P(getting a diamond card in 3 trials)

$=\dfrac{13}{52}+\dfrac{39}{52}\times \dfrac{13}{52}+(\dfrac{39}{52})^2\times \dfrac{13}{52} \\=\dfrac{13}{52}(1+\dfrac{39}{52}+(\dfrac{39}{52})^2) \\=\dfrac{37}{64}$