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The king, queen and jack of clubs are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of

(i) heart

(ii) queen

(iii) clubs.

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2 Answers

Total no. of remaining cards = 52 – 3 = 49

(i) E⟶ event of getting hearts

No. of favorable outcomes = 3 {4 – 1}

Probability, P(E) = (No.of favorable outcomes)/(Total no.of possible outcomes)

P(E) = 13/49

(ii) E ⟶ event of getting queen

No. of favorable outcomes = 3 (4 – 1) {Since queen of clubs is removed}

P(E) = 3/49

(iii) E ⟶ event of getting clubs

No. of favorable outcomes = 10 (13 – 3) {Since 3 club cards are removed}

P(E) = 10/49

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Total number of possible outcomes, n(S) = 52 – 3 = 49 

(i) Number of favorable outcomes, 

n(E) = 13

∴ P(E) =  \(\frac{n(E)}{n(S)}\) = \(\frac{13}{49}\)

(ii) Number of favorable outcomes, n(E) = 4 – 1 = 3

 ∴ P(E) =  \(\frac{n(E)}{n(S)}\) = \(\frac{3}{49}\)

(iii) Number of favorable outcomes, n(E) = 13 – 3 = 10

  ∴ P(E) =  \(\frac{n(E)}{n(S)}\) = \(\frac{10}{49}\)

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