Question

A card is drawn from a well shuffled deck of playing cards. Find the probability that the card drawn is (i) a face card (ii) red colour face card (iii) black colour face card .

Answer 1

A deck of playing cards consists of 52 cards out of which 26 are black cards and  other 26 are red cards, where red cards consists of 13 cards of heart , 13 cards of diamond and black cards consists of 13 cards  of spades and 13 cards are club.

13 cards in each suit are king ,queen, Jack, 10, 9,8,7,6, 5, 4, 3 and 2.
King, queen ,and jack are called face cards. Total number of face cards are 12.

SOLUTION:
Total number of outcomes = 52

i) Favourable outcomes = 12 cards are of face cards
Number of favourable outcomes= 12

Probability = Number of favourable outcomes/ Total number of outcomes.

Required probability = P(face card) = 12/52= 3/13
Hence, the probability that the card  drawn is face card 3/13.

ii) Total number of red face card= 3+3=6
Number of favourable outcomes= 6

Probability = Number of favourable outcomes/ Total number of outcomes.

Required probability = P(red face card) = 6/52= 3/26
Hence, the probability that the card  drawn is red face card 3/26.

iii) Total number of black face card= 3+3=6
Number of favourable outcomes= 6

Probability = Number of favourable outcomes/ Total number of outcomes.

Required probability = P(black face card) = 6/52= 3/26
Hence, the probability that the card  drawn is black face card 3/26.

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Answer 2

SOLUTION:
Total number of outcomes = 52

i) Favourable outcomes = 12 cards are of face cards
Number of favourable outcomes= 12

Probability = Number of favourable outcomes/ Total number of outcomes.

Required probability = P(face card) = 12/52= 3/13
Hence, the probability that the card  drawn is face card 3/13.

ii) Total number of red face card= 3+3=6
Number of favourable outcomes= 6

Probability = Number of favourable outcomes/ Total number of outcomes.

Required probability = P(red face card) = 6/52= 3/26
Hence, the probability that the card  drawn is red face card 3/26.

iii) Total number of black face card= 3+3=6
Number of favourable outcomes= 6

Probability = Number of favourable outcomes/ Total number of outcomes.

Required probability = P(black face card) = 6/52= 3/26
Hence, the probability that the card  drawn is black face card 3/26.