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

Answer 1

Let S denote the sample space. Then, n(S) = 52.
(i) Let `E_(1) =` event of drawing an ace.
Since, the number of all aces is 4, so `n(E_(1)) = 4.`
`therefore` P(getting an ace) `= P(E_(1)) = (n(E_(1)))/(n(S)) = 4/52 = 1/13.`
(ii) Let `E_(2) =` event of getting a heart. Then, `n(E_(2)) = 13.`
`therefore` P(getting an heart) `P(E_(2)) = (n(E_(2)))/(n(S)) = 13/52 = 1/4`.
(iii) Let `E_(3) =` event of getting an eight of hearts. Then, `n(E_(3)) = 1`.
`therefore` P(getting an eight of hearts) `= P(E_(3)) = (n(E_(3)))/(n(S)) = 1/52.`
(iv) Let `E_(4) =` event of getting a club. Then, `n(E_(4)) = 13`.
`therefore` P(getting a club) `= P(E_(4)) = (n(E_(4)))/(n(S)) = 13/52 = 1/4`.
(v) Let `E_(5) =` event of getting a red card. Then, `n(E_(5)) = 26`.
`therefore` P(getting a red card) `= P(E_(5)) = (n(E_(5)))/(n(S)) = 26/52 = 1/2.`
(vi) Let `E_(6) =` event of getting a face card. Then, `n(E_(6)) = 16`.
`therefore` P(getting a red card) `= P(E_(6)) = (n(E_(6)))/(n(S)) = 16/52 = 4/13.`
(vii) Let `E_(7) =` event of getting a diamond. Then, `n(E_(7)) = 13`.
`therefore` P(getting a diamond) `= P(E_(7)) = (n(E_(7)))/(n(S)) = 13/52 = 1/4.`
(viii) Let `E_(8) =` event of getting a jack. Then, `n(E_(8)) = 4`.
`therefore` P(getting a jack) `= P(E_(8)) = (n(E_(8)))/(n(S)) = 4/52 = 1/13.`
(ix) Let `E_(9) =` event of getting a black card. Then, `n(E_(9)) = 26`.
`therefore` P(getting a black card) `= P(E_(9)) = (n(E_(9)))/(n(S)) = 26/52 = 1/2.`