# Aptitude - Probability - Discussion

Discussion Forum : Probability - General Questions (Q.No. 13)
13.
Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:
 3 20
 29 34
 47 100
 13 102
Explanation:

Let S be the sample space.

 Then, n(S) = 52C2 = (52 x 51) = 1326. (2 x 1)

Let E = event of getting 1 spade and 1 heart. n(E) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13 = (13C1 x 13C1) = (13 x 13) = 169. P(E) = n(E) = 169 = 13 . n(S) 1326 102

Discussion:
41 comments Page 1 of 5.

Deepika said:   4 months ago
We have only 4 hearts in total in a deck of 52 cards. So, shouldn't it be 4C1? Why are we using 13C1 for hearts?

Rangesh said:   2 years ago
@ALL.

Total pack of cards 52.
One card from the heart so spade contains 13cards.

Use C method.

One card from spade and (*) one card from heart =13C1 * 13C1.
Total cards to be picked =2, so 52C2= (52*51)Ã·(1*2).

Now simplify

(13C1*13C1)Ã·(52*51 /1*2).

If we simply the common terms we get.
13/2*51 =13/102.

By simplifying, we will get the answer.

ARNAV said:   2 years ago
The answer over here is wrong.

As it is mentioned we should be adding.

(13c1+13c1) / 52c2.

Sofiya said:   2 years ago
Why can't it be 13c2*13c2/52?

Can anyone give me a proper explanation?

Satya said:   3 years ago
@Priya & @Shekhar.

26C2 would mean that you may choose any 2 cards out of 26 cards(13 spade+ 13 heart)
i.e. both the cards may be the heart (for ex.) which would be wrong.

Sudhakar said:   4 years ago
How to get 102?

The probability of cards 52C2=52*51/2*1 = 1326.
The cards spade and heart 13C1*13C1 = 169.
169/1326 = 13/12.
(1)

Kalai said:   4 years ago

Because you can possible to divide it(169/1326)using by 13.
13*13 = 169.
13*102=1326, So, the answer is 13/1326.

HARSHA said:   5 years ago
Here how we got 13?

Junaidh said:   5 years ago
First card taken can be spade or heart. So the probability is 26/52.

So the second card should be from the other set (spade or heart). Probability for that is 13/51. So, totally, (26/52)*(13/51) = 13/102.
(12)

Sasi said:   5 years ago
Why not adding two type of cards as 26c2?