Question

From a pack of 52 playing cards Jacks, queens, kings and aces of red colour are removed. From the remaining, a card is drawn at random. Find the probability that the card drawn is 

(i) a black queen 

(ii) a red card 

(iii) a black jack 

(iv) a picture card (Jacks, queens and kings are picture cards).

Answer 1

Total number of possible outcomes, n(S) = 52 – 2 – 2 – 2 – 2 = 44 

(i) Number of favorable outcomes, 

n(E) = 2

∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{2}{44}\) = \(\frac{1}{22}\)

(ii) Number of favorable outcomes, n(E) = 26 – 8 = 18

∴ P(E) = \(\frac{n(E)}{n(S)}\)  = \(\frac{18}{44}\) = \(\frac{9}{22}\)

(iii) Number of favorable outcomes, 

n(E) = 2

∴ P(E) = \(\frac{n(E)}{n(S)}\)  = \(\frac{2}{44}\) = \(\frac{1}{22}\)

(iv) Number of favorable outcomes, 

n(E) = 6

∴ P(E) = \(\frac{n(E)}{n(S)}\)  = \(\frac{6}{44}\) = \(\frac{3}{22}\)