Question

You shuffle a standard deck of 52 playing cards and draw two cards. Let X be...

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.

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Answer #1

Total number of cards = 52

Total number of diamonds= 13

Total number of non diamonds cards = 39

Let X be tge random variable denoting the number of diamonds in the two selected cards

X= 0, 1,2

P( X=0) = P( first card is Non diamond) * P( second card is non diamiond)

= (39/52) * ( 38/51)

= 0.5588

P( X=1)= P( first card is diamond) * P( second card is non diamiond) + P( first card is Non diamond) * P( second card is diamiond)

= (13/52) (39/51) + (39/52) (13/51)

= 0.1912

P( X=2) = P( first card is diamond) * P( second card is diamiond)

= (13/52) * (12/51)

= 0.0588

X 0 1 2
P(X=x) 0.5588 0.1912 0.0588
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