### Discussion :: Probability - General Questions (Q.No.13)

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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