All the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Giving ace a value 1 similar value for other cards, find the probability that the card has a value

(i) 7
(ii) greater than 7
(iii) less than 7

Answers (1)

(i) Answer. [1/10]
Solution. Probability; Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one
Total cards = 52 – 12 = 40      ( 12 cards are removed)
card with number 7 = 4
favourable cases = 4
probability = \frac{Number\, of\, favourable\ cases }{Total\, number\, of\, cases}
Probability of getting card  7= \frac{4}{10}= \frac{1}{10}

 
(ii) Answer. [3/10]
Solution. Probability; Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one
Total cards = 52 – 12 = 40      (\mathbb{Q}  12 cards are removed)
Cards greater than 7 =8,9,10 (3 × 4 = 12)
favourable cases = 12
probability = \frac{Number\, of\, favourable\ cases }{Total\, number\, of\, cases}
Probability of getting card  7= \frac{12}{40}= \frac{3}{10}
 
(iii) Answer. [3/5]
Solution. Probability; Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one
Total cards = 52 – 12 = 40      (\because  12 cards are removed)
Cards less than 7 = 1, 2, 3, 4, 5, 6                 (6 × 4 = 24)
favourable cases = 24
probability = \frac{Number\, of\, favourable\ cases }{Total\, number\, of\, cases}
Probability of getting card  7= \frac{24}{40}= \frac{6}{10}= \frac{3}{5}

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