Answer :

In a deck of 52 cards, there are 4 aces each of one suit respectively.


Let X be the random variable denoting the number of aces for an event when 4 cards are drawn simultaneously.


X can take values 0 , 1 , 2 , 3 or 4


P(X = 0) =


[For selecting 0 aces, we removed all 4 aces from the deck and selected out of 48]


P(X = 1) =


[For selecting 1 ace, we selected and 1 out of 4aces and 3 cards from remaining 48]


P(X = 2) =


[For selecting 2 aces, we selected and 2 out of 4aces and 2 cards from remaining 48]


P(X = 3) =


[For selecting 3 aces, we selected and 3 out of 4aces and 1 card from remaining 48]


P(X = 4) =


[For selecting 4 aces, we selected and 4 out of 4 aces]


Now we have pi and xi.


Now we are ready to write the probability distribution for X:-


The following table gives probability distribution:



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