Question

Amar keeps picking playing cards out of a standard deck of 52 cards in hopes that he will draw a spade. There are 13 spades in the deck. After looking at each card, he places it back in the deck. What is the probability that Amar will draw a spade in the first five attempts?

A) 24%

B) 45%

C) 76%

D) 81%

Answer 1

P(drawing a spade) = 13/52 = 1/4 = 0.25

P(X < 5) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

              = 0.25 + (1 - 0.25) * 0.25 + (1 - 0.25)² * 0.25 + (1 - 0.25)³ * 0.25 + (1 - 0.25)⁴ * 0.25

              = 0.7627

              = 76%

Option-C) 76%