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The question given below consists of a statement and /or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question. A card is picked at random from a well shuffled regular pack of cards. What card is it? I. If another card is drawn without replacement, the probability that it is a red queen is not 2/51 II. If another card is drawn without replacement, the probability that it is not a diamond is 13/17

The question given below consists of a statement and /or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question. A card is picked at random from a well shuffled regular pack of cards. What card is it? I. If another card is drawn without replacement, the probability that it is a red queen is not 2/51 II. If another card is drawn without replacement, the probability that it is not a diamond is 13/17 Correct Answer BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, bu tNEITHER statement ALONE is sufficient

From statement I:

If the card drawn is not a black queen, then there are 2 red queens left in the pack

When another card is drawn, the probability of getting a red queen would be 2/51

So, using I alone, we know that the card picked was a red queen but we do not know exactly which suit it belongs to

From statement II:

The probability that the second card is of diamonds is 1 - (13/17) = 4/17 = 12/51

That means that there are 12 cards of diamonds left in the pack. So, we know that the first card was of diamonds

Using I and II together we can conclude that the 1st card was the queen of diamonds

∴ Option 3 is the correct answer

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