Let two cards are drawn at random from a pack of 52 playing cards. Let X be the number of aces obtained. Then the values of E ( X ) is

Step-by-step solution

' X ' can take values 0.1 .2 . Probability of getting no ace card. = ⁴⁸ C ₂ ⁵² C ₂ = 48 ! 2 ! 46 ! 2 ! 50 ! 52 ! = 188 221 Probability of getting 1 ace card = ^4 C ₁ ⁴⁸ C ₁ ⁵² C ₂ = 4 48 52 ! 2 ! 50 != 32 221 Probability of getting 2 ace cards aligned & = ^4 C ₂ ⁴⁸ C ₁ ⁵² C ₂ = 4 ! 2 ! 2 ! 2 ! 50 ! 52 ! = 1 221 & E ( X )= p _ i x _ i & =(0) ( 188 221 )+(1) ( 32 221 )+(2) ( 1 221 )= 2 13 aligned