Three cards are drawn from a standard deck of 52 cards. What is the possibility that a jack, a queen, and a king are selected, drawn in succession without?

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Answer 1 · 2017-03-28T14:17:09

#8/15675.#

Let, #J=# the Event that a Jack has been selected from a std.

deck.

#Q and K# denote similar Events for Queen and King resp.

A std. deck have a total of #52# cards in which, #4# are Jacks.

Hence, Prob. of drawing a Jack in the first run, is given by,

#P(J)=4/52........(1).#

Now, for the event #Q,# the Jack card drawn while occurence of

#J# is not to be replaced back in the deck, the deck is left with

#52-1=51# cards with #4# Queens in it.

Therefore, the Prob. of getting a Quuen in the second draw, having

known that the event #J# has occurred, is given by,

#P(Q/J)=4/51...........(2).#

On a similar arguement, we find, #P(K/(QnnJ))=4/50.........(3).#

Now, the Reqd. Prob.#=P(JnnQnnK)#

#=P(J)P(Q/J)P(K/(QnnJ))=(4/52)(4/51)(4/50)=8/15675.#

Enjoy Maths.!