You are dealt 5 cards from a standard and shuffled deck of playing cards. (52 cards) what is the probability that you’ll have at most three kings in your hand?

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Please explain how I would get this! Thanks

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Answer 1 · 2017-12-07T07:52:21

See expplanation.

This probability can be calculated using opposite events.

The opposite events are:

#A# - having at most three kings (0,1,2 or 3)

#A'# - having all 4 kings

The probability #P(A')# is:

#P(A')=48/(C""_52^5)=48/((52!)/((5!)*(47!)))#

#P(A)=48-:((48*49*50*51*52)/(2*3*4*5))#

#P(A)=48-:(4*49*5*51*52)=12/(5*49*51*52)=#

#=3/(5*13*49*51)=1/(5*13*49*17)=1/54145#

So the probability of having at most 3 kings is:

#P(A')=1-P(A)=54144/54145#