Sarthaks Test
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A card is drawn at random from a pack of 52 cards. Find the probability that card drawn is

(i) a black king

(ii) either a black card or a king

(iii) black and a king

(iv) a jack, queen or a king

(v) neither a heart nor a king

(vi) spade or an ace

(vii) neither an ace nor a king

(viii) neither a red card nor a queen

(ix) other than an ace

(x) a ten

(xi) a spade

(xii) a black card

(xiii) the seven of clubs

(xiv) jack

(xv) the ace of spades

(xvi) a queen

(xvii) a heart

(xviii) a red card

1 Answer

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Best answer

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

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