Question

From a well-shuffled deck of 52 cards, a card is picked at random. (i) Find the probability of the card being a queen of spades. (ii) If the card drawn at first is a queen of spade and is not replaced, what is the probability of getting a card which is a spade?

• A. (i) $\frac{1}{52}$ (ii) $\frac{12}{51}$
• B. (i) $\frac{13}{52}$ (ii) $\frac{1}{51}$
• C. (i) $\frac{1}{4}$ (ii) $\frac{1}{12}$
• D. (i) $\frac{1}{26}$ (ii) $\frac{12}{51}$

Answer 1

The correct option is A

(i) $\frac{1}{52}$ (ii) $\frac{12}{51}$

In a well-shuffled card, there are 4 queens and one of them is spade.
There is only one queen of spade in a pack of 52.
(i) So P(Getting a queen of Spade) = $\frac{1}{52}$
Since the first card is a spade and is not replaced, there are only 12 spades left out of 51 cards
(ii) So, P(Getting a spade) = $\frac{12}{51}$