Given: Two cards are taken together out of a pack of 52 cards Concept used: Classical definition of probability. Formula used: Probability =
Favorable‌Outcome
Total‌Outcome
. P(E) =
n(E)
n(S)
nCr =
n!
r!(n−r)!
Calculation: n(S) = Total number of ways of drawing 2 cards from 52 cards = 52C2 Let E be event of getting 1 spade and 1 heart. We know that there are 13 spades and 13 hearts in the total 52 cards. ⇒ 13C1 × 13C1 P (E) =
n(E)
n(S)
⇒
13C1×13C1
C2
⇒
(13×13)
(52×51)
(1×2)
⇒
169
1326
⇒
13
102
∴ The probability that one card is a spade and the other is a heart is