From a pack of 52 playing cards Jacks, queens, kings and aces of red c

1.	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» 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) = \(\frac{n(E)}{n(S)}\) = \(\frac{6}{44}\) = \(\frac{3}{22}\)

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»

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

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