Aptitude - Probability - Discussion

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.

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.

@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)÷(1*2).

Now simplify

(13C1*13C1)÷(52*51 /1*2).

If we simply the common terms we get.
13/2*51 =13/102.

By simplifying, we will get the answer.

@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).

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.

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

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.

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?

@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.

@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.