Question

(1) You keep drawing a pair of cards (all at once and therefore without replacement) from a well-shuffled deck of 52 cards until both cards turn out to be aces. What are the chances that you (a) succeed at the very first attempt? (b) need more than 10 attempts? (b) need at most 4 attempts?

Answer 1

a)probability of drawing a pair of ace in first attempt =P(select 2 ace from 4) =(4/52)*(3/51)=1/221

b)

P(need more than 10 attempts) =P(failed in first 10 attempts) =(1-1/221)¹⁰ =0.9557

c)

P( need at most 4 attempts )=1-P(failed in first 10 attempts) =1-(1-1/221)⁴ =1-0.9820 =0.0180