Question

Two cards are drawn from a well shuffled pack of 52 cards without replacement. The probability of drawing a queen and a jack is :

• A. $\frac{16}{663}$
• B. $\frac{2}{663}$
• C. $\frac{4}{663}$
• D. $\frac{8}{663}$

Answer 1

Answer: (C)

$\frac{4}{663}$

2 cards may be taken out of a deck of 52 cards in $C_2^{52}$ ways.

$\therefore$ The total number of elementary events

=$C_2^{52}=51\times 52$.
There are $4$ queens & $4$ jacks in a pack.

Then, 4 Queens can be drawn in $C_4^4=4$ ways and

$4$ Jacks can be drawn in $C_4^4=4$ ways .

$\therefore$ The total number of ways

ie .the total number of favorable events=$4\times 4=16$.

So the probability of getting 1 Queen and 1 Jack

=$\frac{numberoffavourableevents}{numberofelementaryevents}=\frac{16}{51\times 52}=\frac{4}{663}$.