Math, asked by vahileabhishek46791, 9 months ago

A card is drawn at random from a pack of 52 cards. Find the probability that the 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
(xix) neither a king nor a queen

Answers

Answered by subhamrout2019

106

Step-by-step explanation:

To find the probability of drawing a particular card in each case :

• Total number of cards in the pack = 52

• Number of spades (black) = 13

Number of clubs (black) = 13

Number of hearts (red) = 13

Number of diamonds (red) = 13

• Probability of an event (P) = Number of favourable outcomes / Total number of possible outcomes

(i) • Probability of drawing a black king (P1) = Number of black kings / Total number of cards in the pack

• Number of black kings = King of spades + King of clubs

= 1 + 1 = 2

• P1 = 2 / 52 = 1 / 26

(ii) • Probability of drawing either a black card or a king (P2) = (Number of black cards + Number of kings in red cards) / Total number of cards

=> P2 = (26 + 2) / 52

Or, P2 = 28 / 52

Or, P2 = 7 / 13

(iii) Probability of drawing a card that is black and a king (P3) = Number of black kings in the pack / Total number of cards in the pack

=> P3 = 2 / 52

Or, P3 = 1 / 26

(iv) Probability of drawing a jack or a queen or a king (P4) = (Number of jacks + Number of queens + Number of kings) / Total number of cards

=> P4 = (4 + 4 + 4) / 52

Or, P4 = 12 / 52

Or, P4 = 3 / 13

(v) • Probability of drawing a heart or a king (Phk) = (Number of hearts + Number of kings in spades, clubs, and diamonds) / Total number of cards

=> Phk = (13 + 3)

Or, Phk = 16 / 52

Or, Phk = 4 / 13

• Now, probability of drawing neither a heart nor a king (P5) = 1 - Probability of drawing a heart or a king

=> P5 = 1 - (4 / 13)

=> P5 = (13 - 4) / 13

=> P5 = 9 / 13

(vi) Probability of drawing a spade or an ace (P6) = (Number of spades + Number of aces in hearts, clubs, amd diamonds) / Total number of cards

=> P6 = (13 + 3) / 52)

Or, P6 = 16 / 52

Or, P6 = 4 / 13

(vii) Probability of drawing neither an ace nor a king (P7) = 1 - Probability of drawing an ace or a king

• Now, probability of drawing an ace or a king (Pak) = (Number of aces + Number of kings) / Total number of cards

=> Pak = (4 + 4) / 52)

Or, Pak = 8 / 52

Or, Pak = 2 / 13

• Therefore, P(7) = 1 - (2 / 13)

=> P7 = (13 - 2) / 13

=> P7 = 11 / 13

(viii) Probability of drawing neither a red card nor a queen (P8) = 1 - Probability of drawing a red card or a queen

• Now, probability of drawing a red card or a queen (Prq) = (Number of red cards + Number of queens in black cards) / Total number of cards

=> Prq = (26 + 2) / 52

Or, Prq = 28 / 52

Or, Prq = 7 / 13

• P8 = 1 - Prq

Or, P8 = 1 - (7 / 13)

Or, P8 = (13 - 7) / 13

Or, P8 = 6 / 13

(ix) Probability of drawing an ace = 4 / 52 = 1 / 13

• Probability of drawing a card other than an ace (P9) = 1 - (1 / 13)

Or, P9 = (13 - 1) / 13

Or, P9 = 12 / 13

(x) Number of tens in the pack = 1 of spade + 1 of club + 1 of heart + 1 of diamond

= 4

Probability of drawing a ten = 4 / 52 = 1 / 13

(xi) Probability of drawing a spade (P11) = Number of spades / Total number of cards

=> P(11) = 13 / 52 = 1 / 4

(xii) Number of black cards = 26

Probability of drawing a black card (P12) = 26 / 52 = 1 / 2

(xiii) Probability of drawing the seven of clubs P(13) = Number of 7 in the club / Total number of clubs

=> P(13) = 1 / 13

(xiv) Probability of drawing a jack (P14) = Number of jacks / Total number of cards

=> P(14) = 4 / 52 = 1 / 13

(xv) Probability of drawing the ace of spades (P15) = Number of aces in the spade / Total number of spades

=> P(15) = 1 / 13

(xvi) Probability of drawing a queen (P16) = Number of queens in the pack / Total number of cards in the pack

=> P(16) = 4 / 52 = 1 / 13

(xvii) Probability of drawing a heart (P17) = Number of hearts in the pack / Total number of cards in the pack

=> P17 = 26 / 52 = 1 / 2

(xviii) Probability of drawing a red card (P18) = Number of red cards in the pack / Total number of cards in the pack

=> P18 = 26 / 52 = 1 / 2

(xix) Probability of drawing neither a king nor a queen (P19) = 1 - Probability of drawing a king or a queen

• Probability of drawing a king or a queen (Pkq) = (Number of kings + Number of queens in the pack) / Total number of cards in the pack

=> Pkq = (4 + 4) / 52

=> Pkq = 8 / 52

=> Pkq = 2 / 13

• Therefore, P19 = 1 - Pkq

=> P19 = 1 - (2 / 13)

Or, P19 = (13 - 2) / 13

Or, P19 = 11 / 13

Answered by Anonymous

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