Aptitude - Probability - Discussion

Discussion :: 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:

[A].
3
20
[B].
29
34
[C].
47
100
[D].
13
102

Answer: Option D

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


Kavitha said: (Feb 4, 2011)  
Why can't it be (13C1 + 13C1) I am getting confused where 2 multiply and where 2 add can any one help me.

Parikshit said: (May 7, 2011)  
The answer should be 13/51.
Both of the following two cases should be considered:
one is spade and the other is heart......and..
one is heart and the other is spade....

so multiply by 2..

Probablity said: (May 8, 2011)  
1st card is a spade = 13/52 AND
2nd card is a heart = 13/51

therefore 13/52 x 13/51 ... (1)

OR

1st card is a heart = 13/52 AND
2nd card is a spade = 13/51

therefore 13/52 x 13/51 ... (2)

Adding 1 & 2 we get 13/102

Mdk said: (Aug 26, 2011)  
Thanks parikshit.

Swetha said: (Nov 8, 2011)  
@kavitha.

In this question, we have to find propability for taking 2 cards one is spade and another one is heart. If and comes, we should multiply likewise if or is given, then we should add.

Xyz said: (Jan 17, 2012)  
@ kavita:
in case of "AND" we have to "multiply"
& in case of "OR" we have to "Add"

Santosh said: (Jan 27, 2012)  
Here actually we discussed earlier as both are same combination we add other wise multiply. So clarify that doubt. I understood this problem but add and multiply explain.

Amol said: (Mar 10, 2012)  
Thanks Probability

Neeta said: (Oct 28, 2012)  
Can anybody explain me how to solve 52C2 ? or such other examples like 7C2, 13C1 etc.

Irfan said: (Nov 7, 2012)  
52C2 = 52/2*51/1 i.e. 1326 Answer.

or

nCr = n!/(r!)(n - r)!

Ali said: (Mar 20, 2013)  
But 13/52 * 13/51 is not equal to 13/102, but rather 13/204.

Karim said: (Jul 29, 2013)  
@Ali, your answer is correct.

The answer should in fact be 13/204 and not 13/102.

You have 13/52 for the first card and for the second it's 13/51.

Multiple together you get 13/204.

Khetesh said: (Nov 28, 2013)  
Actually answer 13/102 is correct.

We draw 2 card:

Possibility of one heart and one spade = (possibility of first spade and second heart) + (possibility of first heart and second spade).

= (13/52)*(13/51) + (13/52)*(13/51).

= 13*13*2/52*51.

= 13/102.

Jayalekshshmi S said: (Jul 8, 2014)  
Number of hearts and spades in a deck of cards is 26. Am I right?

Vinay said: (Jul 8, 2014)  
Probability of A and B = P(a) * P(b).
Probability of A or B = P(a) + P(b).

So, 13/204 is correct, no ?

Sulagna said: (Aug 2, 2014)  
If we are supposed to multiply 13/204 into 2, because w are considering 2 events= 1st spade 2nd heart and 2nd heart, 1st spade, then in the coloured marbles question, why don't we apply the same logic?

Dhruvil said: (Aug 19, 2014)  
Probability = (13+13)/(52*51) = 26/(52*51) = 1/102.

As there are 13 spade cards and 13 heart cards in each pack of 52 cards.

Priya said: (Sep 7, 2014)  
Why can't it be 26C2/52C2?

Shekhar said: (Sep 9, 2014)  
Why can't this be done ?

26P2/52C2 ?

Can anyone please give me a proper explanation.

Anamika said: (Jul 18, 2015)  
The probability of getting spades and hearts why not 26C52+26C51. Because spades and hearts may be from red and black colours of cards.

Naj said: (Nov 3, 2015)  
Why do we have to divide (52 x 51) by 2?

Farheen said: (Sep 25, 2016)  
P(c) = n(c)/n(s).
= 1/52 a king of hearts . Is it true?

Harish said: (Dec 11, 2016)  
Answer should be probability = 13/51.

Aisha said: (Jan 30, 2017)  
From where did 13 come? Can anyone explain? please.

Vineet Pandey said: (Jan 30, 2017)  
Firstly see the question.

In a pack of 52 cards, there are 13 spades and 13 heart.
So, now according to question.

probability of getting 1 spades is =13c1 and same probability of getting heart is also 13c1
Here we write 13c1 because we have to pick a single(1) card out of total spade (13) and use same concept in heart.

Now (13c1 * 13c1 )/ 52c2.
So, the answer is 13/102.

52c2 is written here because there are total 52 cards out of which we pick two(2) card{ 1 of spade and 1 of heart } so that's why it is written as 52c2.

Ashish said: (Feb 12, 2017)  
Thanks @Vineet.

Uchenna said: (Jul 21, 2017)  
Does it mean that every pack must have 13 spade and 13 hearts?

Vanamala Srinivas said: (Dec 8, 2017)  
No, the correct answer is 3/102.

Qaisara said: (Dec 16, 2017)  
I am unable to understand about 13. So anyone please explain me.

Rishit said: (May 2, 2018)  
@Ali and @Karim.

Here 2 cards are drawn TOGETHER. Which is why the 52c2. Your answer is correct for a scenario if the question was first drawn is club and second drawn is heart or vice versa.

Vedant said: (May 14, 2018)  
It is very helpful explanation, Thanks @Khetesh.

Sasi said: (Aug 12, 2018)  
Why not adding two type of cards as 26c2?

Junaidh said: (Aug 18, 2018)  
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.

Harsha said: (Dec 8, 2018)  
Here how we got 13?

Kalai said: (Aug 6, 2019)  
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.

Sudhakar said: (Aug 23, 2019)  
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.

Satya said: (Oct 29, 2020)  
@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).

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