# 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
Answer: Option
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:
42 comments Page 1 of 5.

Arshath Ahamed A said:   2 weeks ago
The answer is Simple,

We need to choose 2 cards one is from spade and another is from heart.

The total cards are 52.

So In the first pick, we will take either spade or heart so the probability is (13 + 13) = 26.

In the second pick, we need to take the rest type (heart or spade) so it is 13 and the total no of cards decreased by 1 due to the first pick.

So the answer is,

P (T) = 26/52 * 13/51,
=> 1/2 * 13/51,
=> 13/102.

Deepika said:   11 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?

Someone, please explain.

Rangesh said:   3 years ago
@ALL.

Total pack of cards 52.
One card from spade so spade contains 13cards.
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:   3 years ago
The answer over here is wrong.

As it is mentioned we should be adding.

(13c1+13c1) / 52c2.

=1/51=> is the correct answer.

Sofiya said:   3 years ago
Why can't it be 13c2*13c2/52?

Can anyone give me a proper explanation?

Satya said:   4 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.

The question specifically asks for 1 spade (from 13 spades) and 1 heart (from 13 heart).

Sudhakar said:   5 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:   5 years ago
Actually answer 13/102 is correct.

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:   6 years ago
Here how we got 13?

Junaidh said:   6 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.
(15)

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