Latest TCS Aptitude Question SOLUTION: @@@@@@@@@@@@@@@@@@@@@@@@@A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both spade. Find the probability of t

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@@@@@@@@@@@@@@@@@@@@@@@@@A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both spade. Find the probability of the lost card being a spade. a. 10/50 b. 10/53 c. 11/50 d. 11/53

Asked In TCS milan jena (8 years ago)

Solved Nancy Read Solution (9)

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pappu mishra  (8 years ago)

total cards:52
drawn cards(spade):2
now, actual present total cards=total cards-drawn cards=52-2=50
total spade=spade-drawn cards(spade)=13-2=11
so,,,probability=11/50

Is this solution Helpfull? Yes (47) | No (1)  

Ranjeet Kumar  (8 years ago)

Remaining spades=11
total cards=50
required prob=11C1/50C1
=

Is this solution Helpfull? Yes (18) | No (5)  

Nancy  (8 years ago) Best Solution

Let S and S1 be the respective events of choosing a spade and a card which is not spade. Let A denote drawing two spades. Out of 52 cards, 13 are spade and 39 cards are not spade.
P(S) = 13/52 = 1/4
P(S1) = 39/52 = 3/4
We first calculate the total probability of drawing two spades when the missing card is a spade and the missing card is not a spade.
Total probability = P(A) = P(S∩A)+P(S1∩A) = P(S).P(AS)+P(S1).P(AS1)
When one spade is lost, there are 12 spades out of 51 cards. Two cards can be drawn out of 12 spade cards in 12C2 ways. Similarly, 2 cards can be drawn out of 51 cards in 51C2 ways.
Probability of drawing 2 spades when one spade is lost = 12C251C2 = 22425
P(S∩A)=P(S).P(AS) = 14×22425
When the lost card is not spade, there are 13 spades out of 51 cards. Two cards can be drawn out of 13 spades in 13C2 ways whereas 2 cards can be drawn out of 51 cards in 51C2 ways.
The probability of getting two cards, when one card is lost which is not spade, is given by P(AS1)
P(AS1) = 13C251C2 = 26425
P(S1∩A)=P(S1).P(AS1) = 34×26425
The probability that the lost card is spade given that two spades are drawn = P(SA) = P(S∩A)P(A) = P(S).P(A/S)P(S).P(A/S)+P(S1).P(A/S1) = 1/4×22/4251/4×22/425+3/4×26/425 = 11/50

Is this solution Helpfull? Yes (13) | No (13)  

Megha  (8 years ago)

As 2 cards are already drawn out which are of spade so spade cards left are 11 out of 13, and from a pack of cards, left cards are 50 out of 52. Thus, the probability of lost card is 11/50 Ans.

Is this solution Helpfull? Yes (4) | No (1)  

ila  (8 years ago)

mbvmbvnmbvnbvnbvnvb

Is this solution Helpfull? Yes (2) | No (28)  

Priya bogra  (8 years ago)

A 10/50 . total spades are 13
2 drawn remaing left are 11 one is lost so prob is 10/50

Is this solution Helpfull? Yes (1) | No (8)  

syed sakirhusain nasirhusain  (8 years ago)

answer is 11/50

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Madhan  (8 years ago)

please dont give such silly questions ,increase intensity
how ever answer is b

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Vijaya Praveena Eranki  (4 years ago)

11/50 option c

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