A card is drawn at random from a well-shuffled deck of 52 cards. Find

1.	A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of getting (i) A queen(ii) A diamond(iii) A king or an ace(iv) A red ace
Answer» Total number of all possible outcomes = 52 (i) Total number of queen = 4 Therefore, P(getting a queen) = \(\frac{4}{52}\) = \(\frac{1}{13}\) (ii) Number of diamond suits = 13 Therefore, P(getting a queen) = \(\frac{13}{52}\) = \(\frac{1}{4}\) (iii) Total number of kings = 4 Let E be the event of getting a king or an ace card. Then, the favorable outcomes = 4 + 4 = 8 Therefore, P(getting a queen) = P(E) = \(\frac{8}{52}\) = \(\frac{2}{13}\) (iv) Number of red aces = 2 Therefore, P(getting a queen) = P(E) = \(\frac{2}{52}\) = \(\frac{1}{26}\)

A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of getting (i) A queen(ii) A diamond(iii) A king or an ace(iv) A red ace

Answer»

Total number of all possible outcomes = 52

(i) Total number of queen = 4

Therefore, P(getting a queen) = \(\frac{4}{52}\) = \(\frac{1}{13}\)

(ii) Number of diamond suits = 13

Therefore, P(getting a queen) = \(\frac{13}{52}\) = \(\frac{1}{4}\)

(iii) Total number of kings = 4

Let E be the event of getting a king or an ace card.

Then, the favorable outcomes = 4 + 4 = 8

Therefore, P(getting a queen) = P(E) = \(\frac{8}{52}\) = \(\frac{2}{13}\)

(iv) Number of red aces = 2

Therefore, P(getting a queen) = P(E) = \(\frac{2}{52}\) = \(\frac{1}{26}\)

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