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A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is: (i) an ace

(ii) a red card

(iii) neither a king nor a queen

(iv) a red face card or an ace

(v) a card of spade

(vi) non-face card of red colour

Answer:

Total number of playing cards = 52 One card is drawn (i) An ace = 4 Therefore, Probability P(E) = 4 / 52 = 1 / 13 (ii) A red card = 13 + 13 = 26 Therefore, Probability P(E) = 26 / 52 = 1 / 2 (iii) Neither a king nor a queen Number of cards = 52 – (4 + 4) = 52 – 8 = 44 Therefore, Probability P(E) = 44 / 52 = 11 / 13 (iv) A red face card = 6 Therefore, Probability P(E) = 6 / 52

= 3 / 26 (v) A card of spade or an ace = 13 + 3 = 16 Therefore, Probability P(E) = 16 / 52 = 4 / 13 (vi) Non-face card of red colour = 26 – 6 = 20 Therefore, Probability P(E) = 20 / 52 = 5 / 13

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