Question

Two card are drawn simultaneously (or successively without replacement) from a well shuffled pack of 52 cards. Find the mean, variance and standard deviation of the number of kings.

Answer 1

Two cards are drawn 

∴ Number of ways that two cards are not king.

= ⁴⁸C₂ = (48 x 47)/2 = 1128

Number of ways of drawing two cards out of 52 cards = ⁵²C₂

= (52 x 51)/2 = 26 x 51 = 1326

∴ Probability of not drawing any king = 1128/1326

Number of way being one king and one not king

⁴C₁ x ⁴⁸C₁ = ⁴C₁ x ⁴⁸C₁ = 4 x 48 = 192

∴ Probability of king and one not king = 192/1326

Number of ways drawing two kings

= ⁴C₂ = (4 x 3)/2 = 6

∴ Probability of being both king = 6/1326

Probability distribution is :