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

Correct option is (c) \(\frac 4{663}\) 

2 cards may be taken out of a deck of 52 cards in C₂⁵²​ ways.

∴ The total number of elementary events

= C₂⁵²

​= 51 × 52.

There are 4 queens & 4 jacks in a pack.

Then, 4 Queens can be drawn in C₄⁴​ = 4 ways and

4 Jacks can be drawn in C₄⁴​ = 4 ways .

∴ The total number of ways  

i.e., the total number of favorable events = 4 × 4 = 16.

So the probability of getting 1 Queen and 1 Jack

\(= \frac{\text{number of faourable events}}{\text{number of elementary events}}\)

\(= \frac{16}{51 \times 52}\)

\(= \frac 4{663}\)

Answer 2

(4/52) (4/51) = 4/663

correct answer is: (c) ⁴/₆₆₃