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Out of a pack of 52 cards one is lost; from the re- mainder of the pack, two cards are drawn and are found to be spades. Find the chance that the missing card is a spade.
  • a)
    11/50
  • b)
    11/49
  • c)
    10/49
  • d)
    10/50
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Out of a pack of 52 cards one is lost; from the re- mainder of the pac...
This problem has to be treated as if we are selecting the third card out of the 50 remaining cards. 11 of these are spades. Hence, 11/50.
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Out of a pack of 52 cards one is lost; from the re- mainder of the pac...

Solution:

Given:
- Total number of cards in the pack = 52
- One card is lost
- Two cards are drawn and found to be spades

Calculating the probability:
- Total number of spades in a deck of 52 cards = 13
- After losing one card, the total number of remaining cards = 51

Probability of drawing two spades:
- Probability of drawing the first spade = 13/51
- Probability of drawing the second spade = 12/50

Using the multiplication rule of probability:
P(both cards are spades) = (13/51) * (12/50) = 156/2550 = 26/425

Probability of missing card being a spade:
- Let the missing card be a spade, then the remaining spades in the pack = 12
- Total possible cases of missing card being a spade = 13

Using the formula for conditional probability:
P(missing card is a spade | both drawn cards are spades) = P(both spades and missing card is spade) / P(both cards are spades)
= (12/51 * 11/50) / (26/425)
= 11/50

Therefore, the chance that the missing card is a spade is 11/50, which corresponds to option 'A'.
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DIRECTIONS for the question:Analyse the graph/s given below and answer the question that follows.A deck of cards has 52 cards, 13 each belonging to four different sets (called suits) viz.; Spades (♠), Hearts (♥), Clubs (♣) and Diamonds (♦). Each card in a set has face value of either one of the numbers 2 to 9 or A or J or Q or K written on it. A is equivalent to number 1, J to 11, Q to 12 and K to 13. The following shows the distribution of the 52 cards among 4 players seated at a table. We name the players North (N), East (E), West (W) and South (S).Q.How many sequences exist with North, West and East? (A sequence is a set of three cards of the same suit that a single person has, the face values in the sequence being consecutiv e). Note: Three of the four cards of a pure sequence should not be counted as a sequence. (in numerical value) Correct answer is '4'. Can you explain this answer?

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Out of a pack of 52 cards one is lost; from the re- mainder of the pack, two cards are drawn and are found to be spades. Find the chance that the missing card is a spade.a)11/50b)11/49c)10/49d)10/50Correct answer is option 'A'. Can you explain this answer?
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