Question

From a well - shuffled deck of 52 cards, a card is drawn at random. Find the probability of getting (i) an ace (ii) a heart (iii) an eight of heart (iv) a club (v) a red card (vi) a face card (vii) a diamond (viii) a jack (ix) a black card Select the correct answer from above options

Answer 1

Let S denote the sample space. Then, n(S) = 52. (i) Let E1= event of drawing an ace. Since, the number of all aces is 4, so n(E1)=4. ∴ P(getting an ace) =P(E1)= n(E1) n(S) = 4 52 = 1 13 . (ii) Let E2= event of getting a heart. Then, n(E2)=13. ∴ P(getting an heart) P(E2)= n(E2) n(S) = 13 52 = 1 4 . (iii) Let E3= event of getting an eight of hearts. Then, n(E3)=1 . ∴ P(getting an eight of hearts) =P(E3)= n(E3) n(S) = 1 52 . (iv) Let E4= event of getting a club. Then, n(E4)=13 . ∴ P(getting a club) =P(E4)= n(E4) n(S) = 13 52 = 1 4 . (v) Let E5= event of getting a red card. Then, n(E5)=26 . ∴ P(getting a red card) =P(E5)= n(E5) n(S) = 26 52 = 1 2 . (vi) Let E6= event of getting a face card. Then, n(E6)=16 . ∴ P(getting a red card) =P(E6)= n(E6) n(S) = 16 52 = 4 13 . (vii) Let E7= event of getting a diamond. Then, n(E7)=13 . ∴ P(getting a diamond) =P(E7)= n(E7) n(S) = 13 52 = 1 4 . (viii) Let E8= event of getting a jack. Then, n(E8)=4 . ∴ P(getting a jack) =P(E8)= n(E8) n(S) = 4 52 = 1 13 . (ix) Let E9= event of getting a black card. Then, n(E9)=26 . ∴ P(getting a black card) =P(E9)= n(E9) n(S) = 26 52 = 1 2 .