A and B draw two cards one after other from a pack of 52 cards. The probability that all four cards of same colour is

Question

A and B draw two cards one after other from a pack of 52 cards. The probability that all four cards of same colour is (A) (1/17 ×7) (B) (46/49 ×17) (C) (92/49 ×17) (D) None of these

Tardigrade Admin · Accepted Answer

n(A) = Number of ways of drawing 4 cards of same colour = 2C1 × 26C2 × 24C2 n(S) = 52C2 × 50C2 ∴ Required probability=( 26C2 × 24C2 ×2/ 52C2 × 50C2) = (92/49 ×17)

Q. $A$ and $B$ draw two cards one after other from a pack of $52$ cards. The probability that all four cards of same colour is

$\frac{1}{17 \times 7}$

$\frac{46}{49 \times 17}$

$\frac{92}{49 \times 17}$

None of these

$n (A) =$ Number of ways of drawing $4$ cards of same colour
$=^{2} C_{1} \times^{26} C_{2} \times^{24} C_{2}$
$n (S) =^{52} C_{2} \times^{50} C_{2}$
$∴$ Required probability $= \frac{^{26} C _{2} \times ^{24} C _{2} \times 2}{^{52} C _{2} \times ^{50} C _{2}} = \frac{92}{49 \times 17}$

Q. A and B draw two cards one after other from a pack of 52 cards. The probability that all four cards of same colour is

17×71​

49×1746​

49×1792​