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Exercise: Sample Spaces and Events · Q13

Q.A card is drawn from a well-shuffled deck of 5252 cards. Let E=E = 'the card is a spade' and F=F = 'the card is a face card (a king, queen or jack of any suit)'. Find n(E)n(E), n(F)n(F) and n(E∩F)n(E \cap F).

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A standard deck has 5252 cards in 44 suits of 1313 each. EE = 'spade' has all 1313 cards of the spade suit, so n(E)=13n(E)=13. FF = 'face card' consists of the King, Queen and Jack of each of the 44 suits, i.e. 33 face values ×\times 44 suits =12= 12 cards, so n(F)=12n(F)=12. E∩FE \cap F = 'a spade that is also a face car …

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