A card is drawn of random from a well shuffled deck of 52 playing card

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

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.

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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