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

$\frac{8}{15675} .$ $8/15675.$

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

deck.

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

A std. deck have a total of $52$ $52$ cards in which, $4$ $4$ 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.!