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:
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.
Junaidh said:
7 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.
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.
(19)
Arshath Ahamed A said:
1 year 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.
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.
(3)
Deepika said:
2 years 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.
Someone, please explain.
(2)
Karim said:
1 decade ago
@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.
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.
(1)
Vineet pandey said:
9 years ago
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.
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.
(1)
Sudhakar said:
6 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.
The probability of cards 52C2=52*51/2*1 = 1326.
The cards spade and heart 13C1*13C1 = 169.
169/1326 = 13/12.
(1)
Satya said:
5 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).
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).
Sofiya said:
4 years ago
Why can't it be 13c2*13c2/52?
Can anyone give me a proper explanation?
Can anyone give me a proper explanation?
Kalai said:
6 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.
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:
7 years ago
Here how we got 13?
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers