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A card is drawn of random from a well shuffled deck of 52 playing cards. Find the probability that the card drawn is:

(i) a diamond

(ii) not a diamond

(iii) a black coloured

(iv) Not a black coloured.

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Best answer

The number of playing cards in a deck = 52.

(i) The number of diamonds cards in the deck = 13.

∴ The probability that the card drawn is a diamonds 

\(\frac { 13 }{ 52 }\) = \(\frac { 1 }{ 4 }\)

(ii) The number of non-diamonds cards 

= 52 – 13 = 39

∴ The probability that the card drawn is not diamonds 

\(\frac { 39 }{ 52 }\) = \(\frac { 3 }{ 4 }\)

(iii) The number of black cards in the deck = 13 spades + 13 clubs = 26.

∴ The probability that the drawn cards is black 

\(\frac { 26 }{ 52 }\) = \(\frac { 1 }{ 2 }\)

(iv) The probability of getting not black card 

= 1 – \(\frac { 1 }{ 2 }\) = \(\frac { 1 }{ 2 }\)

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