Two cards are drawn at random from a pack of 52 cards. The probability of getting at least a spade and an ace, is

Question

Two cards are drawn at random from a pack of 52 cards. The probability of getting at least a spade and an ace, is (A)  (1/34)  (B)  (8/221)  (C)  (1/26)  (D)  (2/51)

Tardigrade Admin · Accepted Answer

Total number of cases, n(s)=55 C2 n(E)= The number of selection of 1 spade, 1 ace from 3 aces or selections of the ace of spade and 1 other spade. 13 C1 × 13 C4+12 C1 × 11 C1=51 ∴ P(E) (51/52 C2)=(1/26)

Q. Two cards are drawn at random from a pack of $52$ cards. The probability of getting at least a spade and an ace, is

$\frac{1}{34}$

$\frac{8}{221}$

$\frac{1}{26}$

$\frac{2}{51}$

Total number of cases, $n (s) = 55 C_{2}$
$n (E) =$ The number of selection of $1$ spade, $1$ ace from $3$ aces or selections of the ace of spade and $1$ other spade.
$13 C_{1} \times 13 C_{4} + 12 C_{1} \times 11 C_{1} = 51$
$∴ P (E) \frac{51}{52 C _{2}} = \frac{1}{26}$

Q. Two cards are drawn at random from a pack of 52 cards. The probability of getting at least a spade and an ace, is

341​

2218​

261​

512​