Question

Two cards are drawn randomly from a well- shuffled deck of 52 cards. If X denotes the number of aces, then find mean of X:

(i) 5/13

(ii) 1/13

(iii) 37/221

(iv) 2/13

Answer 1

Answer is (iv)

Two cards are drawn randomly from 52 cards, firstly number of total ways that two cards are not an ace.

= ⁴⁸C₂ = (48 x 47)² = 1128

Number of ways drawing 2 cards out of 52 cards

= ⁵²C₂ = (52 x 51)² = 1326

∴ P(X = 0), Probability that no ace is not drawn = 1128/1326

Secondly number of ways that there is an ace and there is no ace out of ⁴C₁ × ⁴⁸C₁