Total no. of outcomes = 52 {52 cards}
(i) E⟶ event of getting a black king
No of favourable outcomes = 2{king of spades & king of clubs}
We know that, P(E) = (No. of favorable outcomes)/(Total no.of possible outcomes) = 2/52 = 1/26
(ii) E⟶ event of getting either a black card or a king.
No. of favourable outcomes = 26 + 2 {13 spades, 13 clubs, king of hearts & diamonds}
P(E) = (26+2)/52 = 28/52 = 7/13
(iii) E⟶ event of getting black & a king.
No. of favourable outcomes = 2 {king of spades & clubs}
P(E) = 2/52 = 1/26
(iv) E⟶ event of getting a jack, queen or a king
No. of favourable outcomes = 4 + 4 + 4 = 12 {4 jacks, 4 queens & 4 kings}
P(E) = 12/52=3/13
(v) E⟶ event of getting neither a heart nor a king.
No. of favourable outcomes = 52 – 13 – 3 = 36 {since we have 13 hearts, 3 kings each of spades, clubs & diamonds}
P(E) = 36/52 = 9/13
(vi) E⟶ event of getting spade or an all.
No. of favourable outcomes = 13 + 3 = 16 {13 spades & 3 aces each of hearts, diamonds & clubs}
P(E) = 16/52 = 4/13
(vii) E⟶ event of getting neither an ace nor a king.
No. of favourable outcomes = 52 – 4 – 4 = 44 {Since we have 4 aces & 4 kings}
P(E) = 44/52 = 11/13
(viii) E⟶ event of getting neither a red card nor a queen.
No. of favourable outcomes = 52 – 26 – 2 = 24 {Since we have 26 red cards of hearts & diamonds & 2 queens each of heart & diamond}
P(E) = 24/52 = 6/13
(ix) E⟶ event of getting card other than an ace.
No. of favourable outcomes = 52 – 4 = 48 {Since we have 4 ace cards}
P(E) = 48/52 = 12/13
(x) E⟶ event of getting a ten.
No. of favourable outcomes = 4 {10 of spades, clubs, diamonds & hearts}
P(E) = 4/52=1/13
(xi) E⟶ event of getting a spade.
No. of favourable outcomes = 13 {13 spades}
P(E) = 13/52 = 1/24
(xii) E⟶ event of getting a black card.
No. of favourable outcomes = 26 {13 cards of spades & 13 cards of clubs}
P(E) = 26/52=1/2
(xiii) E⟶ event of getting 7 of clubs.
No. of favourable outcomes = 1 {7 of clubs}
P(E) = 1/52
(xiv) E⟶ event of getting a jack.
No. of favourable outcomes = 4 {4 jack cards}
P(E) = 4/52=1/13
(xv) E⟶ event of getting the ace of spades.
No. of favourable outcomes = 1{ace of spades}
P(E) = 1/52
(xvi) E⟶ event of getting a queen.
No. of favourable outcomes = 4 {4 queens}
P(E) = 4/52 = 1/13
(xvii) E⟶ event of getting a heart.
No. of favourable outcomes = 13 {13 hearts}
P(E) = 13/52 = 1/4
(xviii) E⟶ event of getting a red card.
No. of favourable outcomes = 26 {13 hearts, 13 diamonds}
P(E) = 26/52 = 1/2
