Two cards are drawn from a well shuffled pack of 52 cards one after an

1.	Two cards are drawn from a well shuffled pack of 52 cards one after another without replacement. Find the probability that one of these is an ace and the other is a queen of the opposite shade.
Answer» Probability of drawing an ace in the first draw = \(\frac{4}{52}.\) Probability of drawing a queen of opposite shade in the second draw = \(\frac{2}{51}.\) Probability of drawing a queen in the first draw = \(\frac{4}{52}.\) Probability of drawing an ace of opposite shade in the second draw = \(\frac{2}{51}.\) ∴ Required probability = \(\frac{4}{52}\) x \(\frac{2}{51}\) + \(\frac{4}{52}\) x \(\frac{2}{51}\) = \(\frac{4}{663}.\) [‘AND’ and ‘OR’Theorems]

Two cards are drawn from a well shuffled pack of 52 cards one after another without replacement. Find the probability that one of these is an ace and the other is a queen of the opposite shade.

Answer»

Probability of drawing an ace in the first draw = \(\frac{4}{52}.\)

Probability of drawing a queen of opposite shade in the second draw = \(\frac{2}{51}.\)

Probability of drawing a queen in the first draw = \(\frac{4}{52}.\)

Probability of drawing an ace of opposite shade in the second draw = \(\frac{2}{51}.\)

∴ Required probability = \(\frac{4}{52}\) x \(\frac{2}{51}\) + \(\frac{4}{52}\) x \(\frac{2}{51}\) = \(\frac{4}{663}.\)

[‘AND’ and ‘OR’Theorems]

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Two cards are drawn from a well shuffled pack of 52 cards one after another without replacement. Find the probability that one of these is an ace and the other is a queen of the opposite shade.

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