Question

You shuffle a standard deck of 52 playing cards and draw two cards. Let X be the random variable denoting the number of diamonds in the two selected cards. Write the probability distribution of X. Recall that there are 13 diamonds in a deck of 52 cards, and that drawing the first and second card are dependent.

Answer 1

• Let X: Number of diamonds drawn out of two draws from a standard deck.
• ^X
• now total ways of drawing 2 cards from 52 cards is =⁵²C₂
• now number of ways of drawing 'X' diamond card( there are 13 diamond cards)=¹³Cx
• if we draw 'X' diamond card then remaining card will be non diamond cards and there are 39 such cards
• so if we draw 'X' diamond card in 2 without replacement draws then '2-X' will be non diamond card and total ways can be (¹³C_x )*(¹⁹C_2-x)
• so total probaility will be= {¹³C_{x *}³⁹C_2-x }divided by(⁵²C₂)