Red queens and black jacks are removed from a pack of 52 playing cards

1.	Red queens and black jacks are removed from a pack of 52 playing cards. A cards is drawn at random from the remaining cards, after reshuffling them. Find the probability that the card drawn is (i) a king (ii) of red colour (iii) a face card (iv) a queen
Answer» Total number of possible outcomes, n(S) = 52 – 2 – 2 = 48 (i) Number of favorable outcomes, n(E) = 4 ∴ P(E) \(\frac{n(E)}{n(S)}\) = \(\frac{4}{48}\) = \(\frac{1}{12}\) (ii) Number of favorable outcomes, n(E) = 24 ∴ P(E) \(\frac{n(E)}{n(S)}\) = \(\frac{24}{48}\) = \(\frac{1}{2}\) (iii) Number of favorable outcomes, n(E) = 12 – 4 = 8 ∴ P(E) \(\frac{n(E)}{n(S)}\) = \(\frac{8}{48}\) = \(\frac{1}{6}\) (iv) Number of favorable outcomes, n(E) = 2 ∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{2}{48}\) = \(\frac{1}{24}\)

Red queens and black jacks are removed from a pack of 52 playing cards. A cards is drawn at random from the remaining cards, after reshuffling them. Find the probability that the card drawn is (i) a king (ii) of red colour (iii) a face card (iv) a queen

Answer»

Total number of possible outcomes, n(S) = 52 – 2 – 2 = 48

(i) Number of favorable outcomes,

n(E) = 4

∴ P(E) \(\frac{n(E)}{n(S)}\) = \(\frac{4}{48}\) = \(\frac{1}{12}\)

(ii) Number of favorable outcomes,

n(E) = 24

∴ P(E) \(\frac{n(E)}{n(S)}\) = \(\frac{24}{48}\) = \(\frac{1}{2}\)

(iii) Number of favorable outcomes, n(E) = 12 – 4 = 8

∴ P(E) \(\frac{n(E)}{n(S)}\) = \(\frac{8}{48}\) = \(\frac{1}{6}\)

(iv) Number of favorable outcomes,

n(E) = 2

∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{2}{48}\) = \(\frac{1}{24}\)

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