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) = ^{52}C_{2} = | (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 |
= (^{13}C_{1} x ^{13}C_{1}) | |
= (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?
Someone, please explain.
Someone, please explain.
Rangesh said:
2 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.
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:
2 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.
As it is mentioned we should be adding.
(13c1+13c1) / 52c2.
=1/51=> is the correct answer.
Sofiya said:
2 years ago
Why can't it be 13c2*13c2/52?
Can anyone give me a proper explanation?
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.
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).
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.
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
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:
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.
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?
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